三角学示例

\frac{\cos (x) \cdot \csc (x)}{\tan (x)}

$\frac{\cos (x) \cdot \csc (x)}{\tan (x)}$

解题步骤 1

分离分数。

\frac{\csc (x)}{1} \cdot \frac{\cos (x)}{\tan (x)}

$\frac{\csc (x)}{1} \cdot \frac{\cos (x)}{\tan (x)}$

解题步骤 2

将

\tan (x)

$\tan (x)$ 重写为正弦和余弦形式。

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

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

解题步骤 3

乘以分数的倒数从而实现除以

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

$\frac{\sin (x)}{\cos (x)}$ 。

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

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

解题步骤 4

将

\cos (x)

$\cos (x)$ 写成分母为

1

$1$ 的分数。

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

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

解题步骤 5

化简。

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解题步骤 5.1

用

\cos (x)

$\cos (x)$ 除以

1

$1$ 。

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

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

解题步骤 5.2

组合

\cos (x)

$\cos (x)$ 和

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

$\frac{\cos (x)}{\sin (x)}$ 。

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

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

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

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

解题步骤 6

用

\csc (x)

$\csc (x)$ 除以

1

$1$ 。

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

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

解题步骤 7

将

\csc (x)

$\csc (x)$ 重写为正弦和余弦形式。

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

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

解题步骤 8

化简分子。

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解题步骤 8.1

对

\cos (x)

$\cos (x)$ 进行

1

$1$ 次方运算。

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

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

解题步骤 8.2

对

\cos (x)

$\cos (x)$ 进行

1

$1$ 次方运算。

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

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

解题步骤 8.3

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

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

解题步骤 8.4

将

1

$1$ 和

1

$1$ 相加。

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

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

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

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

解题步骤 9

合并分数。

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解题步骤 9.1

合并。

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

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

解题步骤 9.2

将

\cos^{2} (x)

$\cos^{2} (x)$ 乘以

1

$1$ 。

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

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

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

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

解题步骤 10

化简分母。

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解题步骤 10.1

对

\sin (x)

$\sin (x)$ 进行

1

$1$ 次方运算。

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

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

解题步骤 10.2

对

\sin (x)

$\sin (x)$ 进行

1

$1$ 次方运算。

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

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

解题步骤 10.3

使用幂法则

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

$a^{m} a^{n} = a^{m + n}$ 合并指数。

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

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

解题步骤 10.4

将

1

$1$ 和

1

$1$ 相加。

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

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

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

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

解题步骤 11

将

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

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

\cot^{2} (x)

$\cot^{2} (x)$ 。

\cot^{2} (x)

$\cot^{2} (x)$

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三角学 示例

三角学示例