初级微积分示例

$\cot (x) \sec^{4} (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1

化简左边。

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解题步骤 1.1

化简 $\cot (x) \sec^{4} (x)$ 。

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解题步骤 1.1.1

将 $\cot (x)$ 重写为正弦和余弦形式。

$\frac{\cos (x)}{\sin (x)} \sec^{4} (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.2

将 $\sec (x)$ 重写为正弦和余弦形式。

$\frac{\cos (x)}{\sin (x)} {(\frac{1}{\cos (x)})}^{4} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.3

化简表达式。

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解题步骤 1.1.3.1

对 $\frac{1}{\cos (x)}$ 运用乘积法则。

$\frac{\cos (x)}{\sin (x)} \cdot \frac{1^{4}}{\cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.3.2

一的任意次幂都为一。

$\frac{\cos (x)}{\sin (x)} \cdot \frac{1}{\cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.4

将 $\frac{\cos (x)}{\sin (x)}$ 乘以 $\frac{1}{\cos^{4} (x)}$ 。

$\frac{\cos (x)}{\sin (x) \cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.5

约去 $\cos (x)$ 和 $\cos^{4} (x)$ 的公因数。

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解题步骤 1.1.5.1

乘以 $1$ 。

$\frac{\cos (x) \cdot 1}{\sin (x) \cos^{4} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.5.2

约去公因数。

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解题步骤 1.1.5.2.1

从 $\sin (x) \cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\frac{\cos (x) \cdot 1}{\cos (x) (\sin (x) \cos^{3} (x))} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.5.2.2

约去公因数。

$\frac{\cos (x) \cdot 1}{\cos (x) (\sin (x) \cos^{3} (x))} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.5.2.3

重写表达式。

$\frac{1}{\sin (x) \cos^{3} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.6

分离分数。

$\frac{1}{\cos^{3} (x)} \cdot \frac{1}{\sin (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.7

将 $\frac{1}{\sin (x)}$ 转换成 $\csc (x)$ 。

$\frac{1}{\cos^{3} (x)} \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.8

组合 $\frac{1}{\cos^{3} (x)}$ 和 $\csc (x)$ 。

$\frac{\csc (x)}{\cos^{3} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.9

从 $\cos^{3} (x)$ 中分解出因数 $\cos (x)$ 。

$\frac{\csc (x)}{\cos (x) \cos^{2} (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.10

分离分数。

$\frac{1}{\cos^{2} (x)} \cdot \frac{\csc (x)}{\cos (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.11

将 $\csc (x)$ 重写为正弦和余弦形式。

$\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\sin (x)}}{\cos (x)} = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.12

将 $\frac{\frac{1}{\sin (x)}}{\cos (x)}$ 重写为乘积形式。

$\frac{1}{\cos^{2} (x)} (\frac{1}{\sin (x)} \cdot \frac{1}{\cos (x)}) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.13

化简。

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解题步骤 1.1.13.1

将 $\frac{1}{\sin (x)}$ 转换成 $\csc (x)$ 。

$\frac{1}{\cos^{2} (x)} (\csc (x) \frac{1}{\cos (x)}) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.13.2

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$\frac{1}{\cos^{2} (x)} (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.14

将 $1$ 重写为 $1^{2}$ 。

$\frac{1^{2}}{\cos^{2} (x)} (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.15

将 $\frac{1^{2}}{\cos^{2} (x)}$ 重写为 ${(\frac{1}{\cos (x)})}^{2}$ 。

${(\frac{1}{\cos (x)})}^{2} (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.16

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$\sec^{2} (x) (\csc (x) \sec (x)) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.17

通过指数相加将 $\sec^{2} (x)$ 乘以 $\sec (x)$ 。

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解题步骤 1.1.17.1

移动 $\sec (x)$ 。

$\sec (x) \sec^{2} (x) \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.17.2

将 $\sec (x)$ 乘以 $\sec^{2} (x)$ 。

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解题步骤 1.1.17.2.1

对 $\sec (x)$ 进行 $1$ 次方运算。

$\sec^{1} (x) \sec^{2} (x) \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.17.2.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

${\sec (x)}^{1 + 2} \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 1.1.17.3

将 $1$ 和 $2$ 相加。

$\sec^{3} (x) \csc (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$

解题步骤 2

因为 $x$ 在方程的右边，所以要交换两边使其出现在方程的左边。

$\cot (x) + 2 \tan (x) + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

解题步骤 3

化简左边。

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解题步骤 3.1

化简每一项。

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解题步骤 3.1.1

将 $\cot (x)$ 重写为正弦和余弦形式。

$\frac{\cos (x)}{\sin (x)} + 2 \tan (x) + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

解题步骤 3.1.2

将 $\tan (x)$ 重写为正弦和余弦形式。

$\frac{\cos (x)}{\sin (x)} + 2 \frac{\sin (x)}{\cos (x)} + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

解题步骤 3.1.3

组合 $2$ 和 $\frac{\sin (x)}{\cos (x)}$ 。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \tan^{3} (x) = \sec^{3} (x) \csc (x)$

解题步骤 3.1.4

将 $\tan (x)$ 重写为正弦和余弦形式。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + {(\frac{\sin (x)}{\cos (x)})}^{3} = \sec^{3} (x) \csc (x)$

解题步骤 3.1.5

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sec^{3} (x) \csc (x)$

解题步骤 4

化简右边。

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解题步骤 4.1

化简 $\sec^{3} (x) \csc (x)$ 。

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解题步骤 4.1.1

将 $\sec (x)$ 重写为正弦和余弦形式。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = {(\frac{1}{\cos (x)})}^{3} \csc (x)$

解题步骤 4.1.2

对 $\frac{1}{\cos (x)}$ 运用乘积法则。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1^{3}}{\cos^{3} (x)} \csc (x)$

解题步骤 4.1.3

一的任意次幂都为一。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x)} \csc (x)$

解题步骤 4.1.4

将 $\csc (x)$ 重写为正弦和余弦形式。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\sin (x)}$

解题步骤 4.1.5

合并。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1 \cdot 1}{\cos^{3} (x) \sin (x)}$

解题步骤 4.1.6

将 $1$ 乘以 $1$ 。

$\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 5

等式两边同时乘以 $\sin (x)$ 。

$\sin (x) (\frac{\cos (x)}{\sin (x)} + \frac{2 \sin (x)}{\cos (x)} + \frac{\sin^{3} (x)}{\cos^{3} (x)}) = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 6

运用分配律。

$\sin (x) \frac{\cos (x)}{\sin (x)} + \sin (x) \frac{2 \sin (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7

化简。

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解题步骤 7.1

约去 $\sin (x)$ 的公因数。

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解题步骤 7.1.1

约去公因数。

$\sin (x) \frac{\cos (x)}{\sin (x)} + \sin (x) \frac{2 \sin (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.1.2

重写表达式。

$\cos (x) + \sin (x) \frac{2 \sin (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.2

乘以 $\sin (x) \frac{2 \sin (x)}{\cos (x)}$ 。

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解题步骤 7.2.1

组合 $\sin (x)$ 和 $\frac{2 \sin (x)}{\cos (x)}$ 。

$\cos (x) + \frac{\sin (x) (2 \sin (x))}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.2.2

对 $\sin (x)$ 进行 $1$ 次方运算。

$\cos (x) + \frac{2 (\sin^{1} (x) \sin (x))}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.2.3

对 $\sin (x)$ 进行 $1$ 次方运算。

$\cos (x) + \frac{2 (\sin^{1} (x) \sin^{1} (x))}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.2.4

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$\cos (x) + \frac{2 {\sin (x)}^{1 + 1}}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.2.5

将 $1$ 和 $1$ 相加。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.3

乘以 $\sin (x) \frac{\sin^{3} (x)}{\cos^{3} (x)}$ 。

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解题步骤 7.3.1

组合 $\sin (x)$ 和 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.3.2

通过指数相加将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 7.3.2.1

将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 7.3.2.1.1

对 $\sin (x)$ 进行 $1$ 次方运算。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{1} (x) \sin^{3} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.3.2.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 7.3.2.2

将 $1$ 和 $3$ 相加。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\cos^{3} (x) \sin (x)}$

解题步骤 8

约去 $\sin (x)$ 的公因数。

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解题步骤 8.1

从 $\cos^{3} (x) \sin (x)$ 中分解出因数 $\sin (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\sin (x) \cos^{3} (x)}$

解题步骤 8.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \sin (x) \frac{1}{\sin (x) \cos^{3} (x)}$

解题步骤 8.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} = \frac{1}{\cos^{3} (x)}$

解题步骤 9

从等式两边同时减去 $\frac{1}{\cos^{3} (x)}$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10

化简每一项。

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解题步骤 10.1

从 $\sin^{2} (x)$ 中分解出因数 $\sin (x)$ 。

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.2

分离分数。

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.3

将 $\frac{\sin (x)}{\cos (x)}$ 转换成 $\tan (x)$ 。

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.4

用 $2 (\sin (x))$ 除以 $1$ 。

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.5

从 $\sin^{4} (x)$ 中分解出因数 $\sin^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.6

乘以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.7

分离分数。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.8

将 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 转换成 $\tan^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 10.9

用 $\sin (x)$ 除以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 11

将方程中的每一项都除以 $\cos (x)$ 。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 12

约去 $\cos (x)$ 的公因数。

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解题步骤 12.1

约去公因数。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 12.2

重写表达式。

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 13

化简分子。

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解题步骤 13.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 13.2

合并指数。

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解题步骤 13.2.1

组合 $\frac{\sin (x)}{\cos (x)}$ 和 $2$ 。

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 13.2.2

组合 $\frac{\sin (x) \cdot 2}{\cos (x)}$ 和 $\sin (x)$ 。

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 13.2.3

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 13.2.4

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 13.2.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 13.2.6

将 $1$ 和 $1$ 相加。

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 14

将分子乘以分母的倒数。

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 15

合并分数。

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解题步骤 15.1

合并。

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 15.2

将 $2$ 乘以 $1$ 。

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 16

化简分母。

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解题步骤 16.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 16.2

将 $1$ 和 $1$ 相加。

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 17

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 18

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 19

分离分数。

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 20

将 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 转换成 $\tan^{2} (x)$ 。

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 21

将 $2$ 乘以 $1$ 。

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 22

用 $2$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 23

化简分子。

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解题步骤 23.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 23.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 24

组合 $\sin (x)$ 和 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 25

通过指数相加将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 25.1

将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 25.1.1

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 25.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 25.2

将 $1$ 和 $3$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 26

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 27

合并。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 28

通过指数相加将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 28.1

将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 28.1.1

对 $\cos (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 28.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 28.2

将 $3$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 29

将 $\sin^{4} (x)$ 乘以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 30

将 $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ 转换成 $\tan^{4} (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 31

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 32

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

解题步骤 33

组合 $\sec (x)$ 和 $\frac{1}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

解题步骤 34

从 $\cos^{3} (x)$ 中分解出因数 $\cos (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

解题步骤 35

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 36

将 $\sec (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 37

将 $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ 重写为乘积形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

解题步骤 38

化简。

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解题步骤 38.1

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

解题步骤 38.2

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 38.3

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 38.4

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 38.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

解题步骤 38.6

将 $1$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 39

将 $1$ 重写为 $1^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 40

将 $\frac{1^{2}}{\cos^{2} (x)}$ 重写为 ${(\frac{1}{\cos (x)})}^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 41

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 42

通过指数相加将 $\sec^{2} (x)$ 乘以 $\sec^{2} (x)$ 。

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解题步骤 42.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

解题步骤 42.2

将 $2$ 和 $2$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

解题步骤 43

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

解题步骤 44

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

解题步骤 45

用 $0$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

解题步骤 46

将 $0$ 乘以 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 47

使用基于 $\tan^{2} (x) + 1 = \sec^{2} (x)$ 恒等式的 $2 (\sec^{2} (x) - 1)$ 替换 $2 \tan^{2} (x)$ 。

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 48

化简每一项。

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解题步骤 48.1

运用分配律。

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 48.2

将 $2$ 乘以 $- 1$ 。

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 49

从 $1$ 中减去 $2$ 。

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 50

重新排列多项式。

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

解题步骤 51

两边同时乘以 $\cos (x)$ 。

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52

化简。

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解题步骤 52.1

化简左边。

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解题步骤 52.1.1

化简 $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ 。

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解题步骤 52.1.1.1

化简每一项。

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解题步骤 52.1.1.1.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.1.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.1.3

组合 $2$ 和 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.1.4

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.1.5

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.1.6

将 $\sec (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.1.7

对 $\frac{1}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.1.8

一的任意次幂都为一。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.2

运用分配律。

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3

化简。

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解题步骤 52.1.1.3.1

将 $\cos (x)$ 乘以 $1$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.2

约去 $\cos (x)$ 的公因数。

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解题步骤 52.1.1.3.2.1

从 $\cos^{2} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.2.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.2.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.3

约去 $\cos (x)$ 的公因数。

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解题步骤 52.1.1.3.3.1

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.3.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.3.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.4

约去 $\cos (x)$ 的公因数。

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解题步骤 52.1.1.3.4.1

将 $- \frac{1}{\cos^{4} (x)}$ 中前置负号移到分子中。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.4.2

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.4.3

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.3.4.4

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.4

将负号移到分数的前面。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5

化简每一项。

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解题步骤 52.1.1.5.1

从 $\sin^{2} (x)$ 中分解出因数 $\sin (x)$ 。

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.2

分离分数。

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.3

将 $\frac{\sin (x)}{\cos (x)}$ 转换成 $\tan (x)$ 。

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.4

用 $2 (\sin (x))$ 除以 $1$ 。

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.5

从 $\sin^{4} (x)$ 中分解出因数 $\sin^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.6

乘以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.7

分离分数。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.8

将 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 转换成 $\tan^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.1.1.5.9

用 $\sin (x)$ 除以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.2

化简右边。

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解题步骤 52.2.1

约去 $\cos (x)$ 的公因数。

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解题步骤 52.2.1.1

约去公因数。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 52.2.1.2

重写表达式。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 53

求解 $x$ 。

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解题步骤 53.1

将方程中的每一项都除以 $\cos (x)$ 。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.2

约去 $\cos (x)$ 的公因数。

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解题步骤 53.2.1

约去公因数。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.2.2

重写表达式。

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.3

化简分子。

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解题步骤 53.3.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.3.2

合并指数。

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解题步骤 53.3.2.1

组合 $\frac{\sin (x)}{\cos (x)}$ 和 $2$ 。

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.3.2.2

组合 $\frac{\sin (x) \cdot 2}{\cos (x)}$ 和 $\sin (x)$ 。

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.3.2.3

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.3.2.4

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.3.2.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.3.2.6

将 $1$ 和 $1$ 相加。

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.4

将分子乘以分母的倒数。

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.5

合并分数。

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解题步骤 53.5.1

合并。

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.5.2

将 $2$ 乘以 $1$ 。

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.6

化简分母。

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解题步骤 53.6.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.6.2

将 $1$ 和 $1$ 相加。

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.7

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.8

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.9

分离分数。

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.10

将 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 转换成 $\tan^{2} (x)$ 。

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.11

将 $2$ 乘以 $1$ 。

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.12

用 $2$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.13

化简分子。

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解题步骤 53.13.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.13.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.14

组合 $\sin (x)$ 和 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.15

通过指数相加将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.15.1

将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.15.1.1

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.15.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.15.2

将 $1$ 和 $3$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.16

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.17

合并。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.18

通过指数相加将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.18.1

将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.18.1.1

对 $\cos (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.18.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.18.2

将 $3$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.19

将 $\sin^{4} (x)$ 乘以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.20

将 $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ 转换成 $\tan^{4} (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.21

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.22

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

解题步骤 53.23

组合 $\sec (x)$ 和 $\frac{1}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.24

从 $\cos^{3} (x)$ 中分解出因数 $\cos (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.25

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.26

将 $\sec (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.27

将 $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ 重写为乘积形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

解题步骤 53.28

化简。

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解题步骤 53.28.1

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

解题步骤 53.28.2

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.28.3

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.28.4

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.28.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

解题步骤 53.28.6

将 $1$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.29

将 $1$ 重写为 $1^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.30

将 $\frac{1^{2}}{\cos^{2} (x)}$ 重写为 ${(\frac{1}{\cos (x)})}^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.31

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.32

通过指数相加将 $\sec^{2} (x)$ 乘以 $\sec^{2} (x)$ 。

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解题步骤 53.32.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

解题步骤 53.32.2

将 $2$ 和 $2$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

解题步骤 53.33

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

解题步骤 53.34

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

解题步骤 53.35

用 $0$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

解题步骤 53.36

将 $0$ 乘以 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.37

使用基于 $\tan^{2} (x) + 1 = \sec^{2} (x)$ 恒等式的 $2 (\sec^{2} (x) - 1)$ 替换 $2 \tan^{2} (x)$ 。

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.38

化简每一项。

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解题步骤 53.38.1

运用分配律。

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.38.2

将 $2$ 乘以 $- 1$ 。

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.39

从 $1$ 中减去 $2$ 。

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.40

重新排列多项式。

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

解题步骤 53.41

两边同时乘以 $\cos (x)$ 。

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42

化简。

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解题步骤 53.42.1

化简左边。

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解题步骤 53.42.1.1

化简 $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ 。

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解题步骤 53.42.1.1.1

化简每一项。

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解题步骤 53.42.1.1.1.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.1.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.1.3

组合 $2$ 和 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.1.4

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.1.5

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.1.6

将 $\sec (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.1.7

对 $\frac{1}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.1.8

一的任意次幂都为一。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.2

运用分配律。

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3

化简。

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解题步骤 53.42.1.1.3.1

将 $\cos (x)$ 乘以 $1$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.2

约去 $\cos (x)$ 的公因数。

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解题步骤 53.42.1.1.3.2.1

从 $\cos^{2} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.2.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.2.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.3

约去 $\cos (x)$ 的公因数。

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解题步骤 53.42.1.1.3.3.1

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.3.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.3.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.4

约去 $\cos (x)$ 的公因数。

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解题步骤 53.42.1.1.3.4.1

将 $- \frac{1}{\cos^{4} (x)}$ 中前置负号移到分子中。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.4.2

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.4.3

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.3.4.4

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.4

将负号移到分数的前面。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5

化简每一项。

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解题步骤 53.42.1.1.5.1

从 $\sin^{2} (x)$ 中分解出因数 $\sin (x)$ 。

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.2

分离分数。

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.3

将 $\frac{\sin (x)}{\cos (x)}$ 转换成 $\tan (x)$ 。

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.4

用 $2 (\sin (x))$ 除以 $1$ 。

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.5

从 $\sin^{4} (x)$ 中分解出因数 $\sin^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.6

乘以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.7

分离分数。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.8

将 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 转换成 $\tan^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.1.1.5.9

用 $\sin (x)$ 除以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.2

化简右边。

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解题步骤 53.42.2.1

约去 $\cos (x)$ 的公因数。

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解题步骤 53.42.2.1.1

约去公因数。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.42.2.1.2

重写表达式。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 53.43

求解 $x$ 。

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解题步骤 53.43.1

将方程中的每一项都除以 $\cos (x)$ 。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.2

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.2.1

约去公因数。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.2.2

重写表达式。

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.3

化简分子。

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解题步骤 53.43.3.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.3.2

合并指数。

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解题步骤 53.43.3.2.1

组合 $\frac{\sin (x)}{\cos (x)}$ 和 $2$ 。

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.3.2.2

组合 $\frac{\sin (x) \cdot 2}{\cos (x)}$ 和 $\sin (x)$ 。

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.3.2.3

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.3.2.4

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.3.2.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.3.2.6

将 $1$ 和 $1$ 相加。

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.4

将分子乘以分母的倒数。

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.5

合并分数。

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解题步骤 53.43.5.1

合并。

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.5.2

将 $2$ 乘以 $1$ 。

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.6

化简分母。

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解题步骤 53.43.6.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.6.2

将 $1$ 和 $1$ 相加。

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.7

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.8

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.9

分离分数。

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.10

将 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 转换成 $\tan^{2} (x)$ 。

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.11

将 $2$ 乘以 $1$ 。

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.12

用 $2$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.13

化简分子。

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解题步骤 53.43.13.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.13.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.14

组合 $\sin (x)$ 和 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.15

通过指数相加将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.43.15.1

将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.43.15.1.1

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.15.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.15.2

将 $1$ 和 $3$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.16

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.17

合并。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.18

通过指数相加将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.43.18.1

将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.43.18.1.1

对 $\cos (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.18.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.18.2

将 $3$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.19

将 $\sin^{4} (x)$ 乘以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.20

将 $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ 转换成 $\tan^{4} (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.21

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.22

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

解题步骤 53.43.23

组合 $\sec (x)$ 和 $\frac{1}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.24

从 $\cos^{3} (x)$ 中分解出因数 $\cos (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.25

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.43.26

将 $\sec (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.43.27

将 $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ 重写为乘积形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

解题步骤 53.43.28

化简。

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解题步骤 53.43.28.1

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

解题步骤 53.43.28.2

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.28.3

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.28.4

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.28.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

解题步骤 53.43.28.6

将 $1$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.29

将 $1$ 重写为 $1^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.30

将 $\frac{1^{2}}{\cos^{2} (x)}$ 重写为 ${(\frac{1}{\cos (x)})}^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.31

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.32

通过指数相加将 $\sec^{2} (x)$ 乘以 $\sec^{2} (x)$ 。

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解题步骤 53.43.32.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

解题步骤 53.43.32.2

将 $2$ 和 $2$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

解题步骤 53.43.33

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

解题步骤 53.43.34

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

解题步骤 53.43.35

用 $0$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

解题步骤 53.43.36

将 $0$ 乘以 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.37

使用基于 $\tan^{2} (x) + 1 = \sec^{2} (x)$ 恒等式的 $2 (\sec^{2} (x) - 1)$ 替换 $2 \tan^{2} (x)$ 。

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.38

化简每一项。

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解题步骤 53.43.38.1

运用分配律。

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.38.2

将 $2$ 乘以 $- 1$ 。

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.39

从 $1$ 中减去 $2$ 。

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.40

重新排列多项式。

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

解题步骤 53.43.41

两边同时乘以 $\cos (x)$ 。

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42

化简。

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解题步骤 53.43.42.1

化简左边。

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解题步骤 53.43.42.1.1

化简 $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ 。

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解题步骤 53.43.42.1.1.1

化简每一项。

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解题步骤 53.43.42.1.1.1.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.1.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.1.3

组合 $2$ 和 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.1.4

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.1.5

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.1.6

将 $\sec (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.1.7

对 $\frac{1}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.1.8

一的任意次幂都为一。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.2

运用分配律。

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3

化简。

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解题步骤 53.43.42.1.1.3.1

将 $\cos (x)$ 乘以 $1$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.2

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.42.1.1.3.2.1

从 $\cos^{2} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.2.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.2.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.3

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.42.1.1.3.3.1

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.3.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.3.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.4

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.42.1.1.3.4.1

将 $- \frac{1}{\cos^{4} (x)}$ 中前置负号移到分子中。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.4.2

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.4.3

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.3.4.4

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.4

将负号移到分数的前面。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5

化简每一项。

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解题步骤 53.43.42.1.1.5.1

从 $\sin^{2} (x)$ 中分解出因数 $\sin (x)$ 。

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.2

分离分数。

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.3

将 $\frac{\sin (x)}{\cos (x)}$ 转换成 $\tan (x)$ 。

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.4

用 $2 (\sin (x))$ 除以 $1$ 。

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.5

从 $\sin^{4} (x)$ 中分解出因数 $\sin^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.6

乘以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.7

分离分数。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.8

将 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 转换成 $\tan^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.1.1.5.9

用 $\sin (x)$ 除以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.2

化简右边。

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解题步骤 53.43.42.2.1

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.42.2.1.1

约去公因数。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.42.2.1.2

重写表达式。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 53.43.43

求解 $x$ 。

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解题步骤 53.43.43.1

将方程中的每一项都除以 $\cos (x)$ 。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.2

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.43.2.1

约去公因数。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.2.2

重写表达式。

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.3

化简分子。

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解题步骤 53.43.43.3.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.3.2

合并指数。

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解题步骤 53.43.43.3.2.1

组合 $\frac{\sin (x)}{\cos (x)}$ 和 $2$ 。

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.3.2.2

组合 $\frac{\sin (x) \cdot 2}{\cos (x)}$ 和 $\sin (x)$ 。

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.3.2.3

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.3.2.4

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.3.2.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.3.2.6

将 $1$ 和 $1$ 相加。

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.4

将分子乘以分母的倒数。

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.5

合并分数。

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解题步骤 53.43.43.5.1

合并。

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.5.2

将 $2$ 乘以 $1$ 。

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.6

化简分母。

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解题步骤 53.43.43.6.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.6.2

将 $1$ 和 $1$ 相加。

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.7

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.8

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.9

分离分数。

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.10

将 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 转换成 $\tan^{2} (x)$ 。

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.11

将 $2$ 乘以 $1$ 。

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.12

用 $2$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.13

化简分子。

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解题步骤 53.43.43.13.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.13.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.14

组合 $\sin (x)$ 和 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.15

通过指数相加将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.43.43.15.1

将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.43.43.15.1.1

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.15.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.15.2

将 $1$ 和 $3$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.16

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.17

合并。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.18

通过指数相加将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.43.43.18.1

将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.43.43.18.1.1

对 $\cos (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.18.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.18.2

将 $3$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.19

将 $\sin^{4} (x)$ 乘以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.20

将 $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ 转换成 $\tan^{4} (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.21

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.22

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.23

组合 $\sec (x)$ 和 $\frac{1}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.24

从 $\cos^{3} (x)$ 中分解出因数 $\cos (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.25

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.26

将 $\sec (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.27

将 $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ 重写为乘积形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.28

化简。

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解题步骤 53.43.43.28.1

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.28.2

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.28.3

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.28.4

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.28.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.28.6

将 $1$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.29

将 $1$ 重写为 $1^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.30

将 $\frac{1^{2}}{\cos^{2} (x)}$ 重写为 ${(\frac{1}{\cos (x)})}^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.31

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.32

通过指数相加将 $\sec^{2} (x)$ 乘以 $\sec^{2} (x)$ 。

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解题步骤 53.43.43.32.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.32.2

将 $2$ 和 $2$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.33

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

解题步骤 53.43.43.34

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

解题步骤 53.43.43.35

用 $0$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

解题步骤 53.43.43.36

将 $0$ 乘以 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.43.37

使用基于 $\tan^{2} (x) + 1 = \sec^{2} (x)$ 恒等式的 $2 (\sec^{2} (x) - 1)$ 替换 $2 \tan^{2} (x)$ 。

$1 + 2 (\sec^{2} (x) - 1) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.43.38

化简每一项。

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解题步骤 53.43.43.38.1

运用分配律。

$1 + 2 \sec^{2} (x) + 2 \cdot - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.43.38.2

将 $2$ 乘以 $- 1$ 。

$1 + 2 \sec^{2} (x) - 2 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.43.39

从 $1$ 中减去 $2$ 。

$2 \sec^{2} (x) - 1 + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.43.40

重新排列多项式。

$\tan^{4} (x) - \sec^{4} (x) + 2 \sec^{2} (x) - 1 = 0$

解题步骤 53.43.43.41

两边同时乘以 $\cos (x)$ 。

$(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42

化简。

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解题步骤 53.43.43.42.1

化简左边。

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解题步骤 53.43.43.42.1.1

化简 $(1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)) \cos (x)$ 。

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解题步骤 53.43.43.42.1.1.1

化简每一项。

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解题步骤 53.43.43.42.1.1.1.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + 2 {(\frac{\sin (x)}{\cos (x)})}^{2} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.1.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + 2 \frac{\sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.1.3

组合 $2$ 和 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \tan^{4} (x) - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.1.4

将 $\tan (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + {(\frac{\sin (x)}{\cos (x)})}^{4} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.1.5

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \sec^{4} (x)) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.1.6

将 $\sec (x)$ 重写为正弦和余弦形式。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - {(\frac{1}{\cos (x)})}^{4}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.1.7

对 $\frac{1}{\cos (x)}$ 运用乘积法则。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1^{4}}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.1.8

一的任意次幂都为一。

$(1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} - \frac{1}{\cos^{4} (x)}) \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.2

运用分配律。

$1 \cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3

化简。

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解题步骤 53.43.43.42.1.1.3.1

将 $\cos (x)$ 乘以 $1$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.2

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.43.42.1.1.3.2.1

从 $\cos^{2} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.2.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} \cos (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.2.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{4} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.3

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.43.42.1.1.3.3.1

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.3.2

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos (x) \cos^{3} (x)} \cos (x) - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.3.3

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.4

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.43.42.1.1.3.4.1

将 $- \frac{1}{\cos^{4} (x)}$ 中前置负号移到分子中。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{4} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.4.2

从 $\cos^{4} (x)$ 中分解出因数 $\cos (x)$ 。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.4.3

约去公因数。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos (x) \cos^{3} (x)} \cos (x) = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.3.4.4

重写表达式。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} + \frac{- 1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.4

将负号移到分数的前面。

$\cos (x) + \frac{2 \sin^{2} (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5

化简每一项。

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解题步骤 53.43.43.42.1.1.5.1

从 $\sin^{2} (x)$ 中分解出因数 $\sin (x)$ 。

$\cos (x) + \frac{2 (\sin (x) \sin (x))}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.2

分离分数。

$\cos (x) + \frac{2 (\sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.3

将 $\frac{\sin (x)}{\cos (x)}$ 转换成 $\tan (x)$ 。

$\cos (x) + \frac{2 (\sin (x))}{1} \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.4

用 $2 (\sin (x))$ 除以 $1$ 。

$\cos (x) + 2 (\sin (x)) \tan (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.5

从 $\sin^{4} (x)$ 中分解出因数 $\sin^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.6

乘以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin^{3} (x) \sin (x)}{\cos^{3} (x) \cdot 1} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.7

分离分数。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \cdot \frac{\sin^{3} (x)}{\cos^{3} (x)} - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.8

将 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 转换成 $\tan^{3} (x)$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \frac{\sin (x)}{1} \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.1.1.5.9

用 $\sin (x)$ 除以 $1$ 。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.2

化简右边。

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解题步骤 53.43.43.42.2.1

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.43.42.2.1.1

约去公因数。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = \frac{0}{\cos (x)} \cos (x)$

解题步骤 53.43.43.42.2.1.2

重写表达式。

$\cos (x) + 2 \sin (x) \tan (x) + \sin (x) \tan^{3} (x) - \frac{1}{\cos^{3} (x)} = 0$

解题步骤 53.43.43.43

求解 $x$ 。

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解题步骤 53.43.43.43.1

将方程中的每一项都除以 $\cos (x)$ 。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.2

约去 $\cos (x)$ 的公因数。

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解题步骤 53.43.43.43.2.1

约去公因数。

$\frac{\cos (x)}{\cos (x)} + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.2.2

重写表达式。

$1 + \frac{2 \sin (x) \tan (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.3

化简分子。

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解题步骤 53.43.43.43.3.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + \frac{2 \sin (x) (\frac{\sin (x)}{\cos (x)})}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.3.2

合并指数。

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解题步骤 53.43.43.43.3.2.1

组合 $\frac{\sin (x)}{\cos (x)}$ 和 $2$ 。

$1 + \frac{\frac{\sin (x) \cdot 2}{\cos (x)} \cdot \sin (x)}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.3.2.2

组合 $\frac{\sin (x) \cdot 2}{\cos (x)}$ 和 $\sin (x)$ 。

$1 + \frac{\frac{\sin (x) \cdot (2 \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.3.2.3

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.3.2.4

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + \frac{\frac{2 (\sin (x) \sin (x))}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.3.2.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{\frac{2 {\sin (x)}^{1 + 1}}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.3.2.6

将 $1$ 和 $1$ 相加。

$1 + \frac{\frac{2 \sin^{2} (x)}{\cos (x)}}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.4

将分子乘以分母的倒数。

$1 + \frac{2 \sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.5

合并分数。

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解题步骤 53.43.43.43.5.1

合并。

$1 + \frac{2 \sin^{2} (x) \cdot 1}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.5.2

将 $2$ 乘以 $1$ 。

$1 + \frac{2 \sin^{2} (x)}{\cos (x) \cos (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.6

化简分母。

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解题步骤 53.43.43.43.6.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + \frac{2 \sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.6.2

将 $1$ 和 $1$ 相加。

$1 + \frac{2 \sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.7

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.8

乘以 $1$ 。

$1 + \frac{2 (\sin^{2} (x) \cdot 1)}{\cos^{2} (x) \cdot 1} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.9

分离分数。

$1 + \frac{2 \cdot (1)}{1} \cdot \frac{\sin^{2} (x)}{\cos^{2} (x)} + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.10

将 $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ 转换成 $\tan^{2} (x)$ 。

$1 + \frac{2 \cdot (1)}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.11

将 $2$ 乘以 $1$ 。

$1 + \frac{2}{1} \cdot \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.12

用 $2$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) \tan^{3} (x)}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.13

化简分子。

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解题步骤 53.43.43.43.13.1

将 $\tan (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) {(\frac{\sin (x)}{\cos (x)})}^{3}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.13.2

对 $\frac{\sin (x)}{\cos (x)}$ 运用乘积法则。

$1 + 2 \tan^{2} (x) + \frac{\sin (x) (\frac{\sin^{3} (x)}{\cos^{3} (x)})}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.14

组合 $\sin (x)$ 和 $\frac{\sin^{3} (x)}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.15

通过指数相加将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.43.43.43.15.1

将 $\sin (x)$ 乘以 $\sin^{3} (x)$ 。

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解题步骤 53.43.43.43.15.1.1

对 $\sin (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin (x) \sin^{3} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.15.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\frac{{\sin (x)}^{1 + 3}}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.15.2

将 $1$ 和 $3$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\frac{\sin^{4} (x)}{\cos^{3} (x)}}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.16

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.17

合并。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.18

通过指数相加将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.43.43.43.18.1

将 $\cos^{3} (x)$ 乘以 $\cos (x)$ 。

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解题步骤 53.43.43.43.18.1.1

对 $\cos (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{3} (x) \cos (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.18.1.2

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{{\cos (x)}^{3 + 1}} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.18.2

将 $3$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x) \cdot 1}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.19

将 $\sin^{4} (x)$ 乘以 $1$ 。

$1 + 2 \tan^{2} (x) + \frac{\sin^{4} (x)}{\cos^{4} (x)} + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.20

将 $\frac{\sin^{4} (x)}{\cos^{4} (x)}$ 转换成 $\tan^{4} (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) + \frac{- \frac{1}{\cos^{3} (x)}}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.21

将分子乘以分母的倒数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \frac{1}{\cos (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.22

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{1}{\cos^{3} (x)} \cdot \sec (x) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.23

组合 $\sec (x)$ 和 $\frac{1}{\cos^{3} (x)}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos^{3} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.24

从 $\cos^{3} (x)$ 中分解出因数 $\cos (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \frac{\sec (x)}{\cos (x) \cos^{2} (x)} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.25

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\sec (x)}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.26

将 $\sec (x)$ 重写为正弦和余弦形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \frac{\frac{1}{\cos (x)}}{\cos (x)}) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.27

将 $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ 重写为乘积形式。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)})) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.28

化简。

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解题步骤 53.43.43.43.28.1

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) (\frac{1}{\cos (x)}))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.28.2

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.28.3

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.28.4

对 $\sec (x)$ 进行 $1$ 次方运算。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot (\sec (x) \sec (x))) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.28.5

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot {\sec (x)}^{1 + 1}) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.28.6

将 $1$ 和 $1$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.29

将 $1$ 重写为 $1^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\frac{1^{2}}{\cos^{2} (x)} \cdot \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.30

将 $\frac{1^{2}}{\cos^{2} (x)}$ 重写为 ${(\frac{1}{\cos (x)})}^{2}$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - ({(\frac{1}{\cos (x)})}^{2} \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.31

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - (\sec^{2} (x) \sec^{2} (x)) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.32

通过指数相加将 $\sec^{2} (x)$ 乘以 $\sec^{2} (x)$ 。

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解题步骤 53.43.43.43.32.1

使用幂法则 $a^{m} a^{n} = a^{m + n}$ 合并指数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - {\sec (x)}^{2 + 2} = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.32.2

将 $2$ 和 $2$ 相加。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{\cos (x)}$

解题步骤 53.43.43.43.33

分离分数。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \frac{1}{\cos (x)}$

解题步骤 53.43.43.43.34

将 $\frac{1}{\cos (x)}$ 转换成 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = \frac{0}{1} \cdot \sec (x)$

解题步骤 53.43.43.43.35

用 $0$ 除以 $1$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0 \sec (x)$

解题步骤 53.43.43.43.36

将 $0$ 乘以 $\sec (x)$ 。

$1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.43.43.37

化简左边。

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解题步骤 53.43.43.43.37.1

化简 $1 + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x)$ 。

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解题步骤 53.43.43.43.37.1.1

使用完全平方法则进行因式分解。

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解题步骤 53.43.43.43.37.1.1.1

将 $1$ 重写为 $1^{2}$ 。

$1^{2} + 2 \tan^{2} (x) + \tan^{4} (x) - \sec^{4} (x) = 0$

解题步骤 53.43.43.43.37.1.1.2

将 $\tan^{4} (x)$ 重写为 ${(\tan^{2} (x))}^{2}$ 。

$1^{2} + 2 \tan^{2} (x) + {(\tan^{2} (x))}^{2} - \sec^{4} (x) = 0$

解题步骤 53.43.43.43.37.1.1.3

请检查中间项是否为第一项被平方数和第三项被平方数的乘积的两倍。

$2 \tan^{2} (x) = 2 \cdot 1 \cdot \tan^{2} (x)$

解题步骤 53.43.43.43.37.1.1.4

重写多项式。

$1^{2} + 2 \cdot 1 \cdot \tan^{2} (x) + {(\tan^{2} (x))}^{2} - \sec^{4} (x) = 0$

解题步骤 53.43.43.43.37.1.1.5

使用完全平方三项式法则对 $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ 进行因式分解，其中 $a = 1$ 和 $b = \tan^{2} (x)$ 。

${(1 + \tan^{2} (x))}^{2} - \sec^{4} (x) = 0$

解题步骤 53.43.43.43.37.1.2

将 $\sec^{4} (x)$ 重写为 ${(\sec^{2} (x))}^{2}$ 。

${(1 + \tan^{2} (x))}^{2} - {(\sec^{2} (x))}^{2} = 0$

解题步骤 53.43.43.43.37.1.3

因为两项都是完全平方数，所以使用平方差公式 $a^{2} - b^{2} = (a + b) (a - b)$ 进行因式分解，其中 $a = 1 + \tan^{2} (x)$ 和 $b = \sec^{2} (x)$ 。

$(1 + \tan^{2} (x) + \sec^{2} (x)) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

解题步骤 53.43.43.43.37.1.4

重新整理项。

$(\tan^{2} (x) + 1 + \sec^{2} (x)) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

解题步骤 53.43.43.43.37.1.5

使用勾股恒等式。

$(\sec^{2} (x) + \sec^{2} (x)) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

解题步骤 53.43.43.43.37.1.6

将 $\sec^{2} (x)$ 和 $\sec^{2} (x)$ 相加。

$2 \sec^{2} (x) (1 + \tan^{2} (x) - \sec^{2} (x)) = 0$

解题步骤 53.43.43.43.37.1.7

重新整理项。

$2 \sec^{2} (x) (\tan^{2} (x) + 1 - \sec^{2} (x)) = 0$

解题步骤 53.43.43.43.37.1.8

使用勾股恒等式。

$2 \sec^{2} (x) (\sec^{2} (x) - \sec^{2} (x)) = 0$

解题步骤 53.43.43.43.37.1.9

从 $\sec^{2} (x)$ 中减去 $\sec^{2} (x)$ 。

$2 \sec^{2} (x) \cdot 0 = 0$

解题步骤 53.43.43.43.37.1.10

乘以 $2 \sec^{2} (x) \cdot 0$ 。

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解题步骤 53.43.43.43.37.1.10.1

将 $0$ 乘以 $2$ 。

$0 \sec^{2} (x) = 0$

解题步骤 53.43.43.43.37.1.10.2

将 $0$ 乘以 $\sec^{2} (x)$ 。

$0 = 0$

解题步骤 53.43.43.43.38

因为 $0 = 0$ ，所以方程对于 $x$ 的所有值将恒成立。

所有实数

解题步骤 54

结果可以多种形式表示。

所有实数

区间计数法：

$(- \infty, \infty)$

初级微积分 示例

初级微积分示例