初级微积分示例

\frac{\sec (x) - \cos (x)}{\tan (x)}

$\frac{\sec (x) - \cos (x)}{\tan (x)}$

解题步骤 1

将

\sec (x)

$\sec (x)$ 重写为正弦和余弦形式。

\frac{\frac{1}{\cos (x)} - \cos (x)}{\tan (x)}

$\frac{\frac{1}{\cos (x)} - \cos (x)}{\tan (x)}$

解题步骤 2

将

\tan (x)

$\tan (x)$ 重写为正弦和余弦形式。

\frac{\frac{1}{\cos (x)} - \cos (x)}{\frac{\sin (x)}{\cos (x)}}

$\frac{\frac{1}{\cos (x)} - \cos (x)}{\frac{\sin (x)}{\cos (x)}}$

解题步骤 3

将分子乘以分母的倒数。

(\frac{1}{\cos (x)} - \cos (x)) \frac{\cos (x)}{\sin (x)}

$(\frac{1}{\cos (x)} - \cos (x)) \frac{\cos (x)}{\sin (x)}$

解题步骤 4

运用分配律。

\frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}

$\frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}$

解题步骤 5

约去

\cos (x)

$\cos (x)$ 的公因数。

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解题步骤 5.1

约去公因数。

\frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}

$\frac{1}{\cos (x)} \cdot \frac{\cos (x)}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}$

解题步骤 5.2

重写表达式。

\frac{1}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}

$\frac{1}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}$

\frac{1}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}

$\frac{1}{\sin (x)} - \cos (x) \frac{\cos (x)}{\sin (x)}$

解题步骤 6

乘以

- \cos (x) \frac{\cos (x)}{\sin (x)}

$- \cos (x) \frac{\cos (x)}{\sin (x)}$ 。

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解题步骤 6.1

组合

\frac{\cos (x)}{\sin (x)}

$\frac{\cos (x)}{\sin (x)}$ 和

\cos (x)

$\cos (x)$ 。

\frac{1}{\sin (x)} - \frac{\cos (x) \cos (x)}{\sin (x)}

$\frac{1}{\sin (x)} - \frac{\cos (x) \cos (x)}{\sin (x)}$

解题步骤 6.2

对

\cos (x)

$\cos (x)$ 进行

1

$1$ 次方运算。

\frac{1}{\sin (x)} - \frac{\cos^{1} (x) \cos (x)}{\sin (x)}

$\frac{1}{\sin (x)} - \frac{\cos^{1} (x) \cos (x)}{\sin (x)}$

解题步骤 6.3

对

\cos (x)

$\cos (x)$ 进行

1

$1$ 次方运算。

\frac{1}{\sin (x)} - \frac{\cos^{1} (x) \cos^{1} (x)}{\sin (x)}

$\frac{1}{\sin (x)} - \frac{\cos^{1} (x) \cos^{1} (x)}{\sin (x)}$

解题步骤 6.4

使用幂法则

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ 合并指数。

\frac{1}{\sin (x)} - \frac{{\cos (x)}^{1 + 1}}{\sin (x)}

$\frac{1}{\sin (x)} - \frac{{\cos (x)}^{1 + 1}}{\sin (x)}$

解题步骤 6.5

将

1

$1$ 和

1

$1$ 相加。

\frac{1}{\sin (x)} - \frac{\cos^{2} (x)}{\sin (x)}

$\frac{1}{\sin (x)} - \frac{\cos^{2} (x)}{\sin (x)}$

\frac{1}{\sin (x)} - \frac{\cos^{2} (x)}{\sin (x)}

$\frac{1}{\sin (x)} - \frac{\cos^{2} (x)}{\sin (x)}$

解题步骤 7

在公分母上合并分子。

\frac{1 - \cos^{2} (x)}{\sin (x)}

$\frac{1 - \cos^{2} (x)}{\sin (x)}$

解题步骤 8

使用勾股恒等式。

\frac{\sin^{2} (x)}{\sin (x)}

$\frac{\sin^{2} (x)}{\sin (x)}$

解题步骤 9

约去

\sin^{2} (x)

$\sin^{2} (x)$ 和

\sin (x)

$\sin (x)$ 的公因数。

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解题步骤 9.1

从

\sin^{2} (x)

$\sin^{2} (x)$ 中分解出因数

\sin (x)

$\sin (x)$ 。

\frac{\sin (x) \sin (x)}{\sin (x)}

$\frac{\sin (x) \sin (x)}{\sin (x)}$

解题步骤 9.2

约去公因数。

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解题步骤 9.2.1

乘以

1

$1$ 。

\frac{\sin (x) \sin (x)}{\sin (x) \cdot 1}

$\frac{\sin (x) \sin (x)}{\sin (x) \cdot 1}$

解题步骤 9.2.2

约去公因数。

\frac{\sin (x) \sin (x)}{\sin (x) \cdot 1}

$\frac{\sin (x) \sin (x)}{\sin (x) \cdot 1}$

解题步骤 9.2.3

重写表达式。

\frac{\sin (x)}{1}

$\frac{\sin (x)}{1}$

解题步骤 9.2.4

用

\sin (x)

$\sin (x)$ 除以

1

$1$ 。

\sin (x)

$\sin (x)$

\sin (x)

$\sin (x)$

\sin (x)

$\sin (x)$

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初级微积分 示例

初级微积分示例