代数示例

\frac{csc (x) cos (x)}{tan (x) + cot (x)}

$\frac{\csc (x) \cos (x)}{\tan (x) + \cot (x)}$

解题步骤 1

将

csc (x)

$\csc (x)$ 重写为正弦和余弦形式。

\frac{\frac{1}{sin (x)} cos (x)}{tan (x) + cot (x)}

$\frac{\frac{1}{\sin (x)} \cos (x)}{\tan (x) + \cot (x)}$

解题步骤 2

化简分母。

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解题步骤 2.1

将

tan (x)

$\tan (x)$ 重写为正弦和余弦形式。

\frac{\frac{1}{sin (x)} cos (x)}{\frac{sin (x)}{cos (x)} + cot (x)}

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

解题步骤 2.2

将

cot (x)

$\cot (x)$ 重写为正弦和余弦形式。

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

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

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

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

解题步骤 3

组合

\frac{1}{sin (x)}

$\frac{1}{\sin (x)}$ 和

cos (x)

$\cos (x)$ 。

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

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

解题步骤 4

将分子乘以分母的倒数。

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

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

解题步骤 5

将

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

$\frac{\cos (x)}{\sin (x)}$ 乘以

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

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

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

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

解题步骤 6

分离分数。

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

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

解题步骤 7

将

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

$\frac{\cos (x)}{\sin (x)}$ 转换成

cot (x)

$\cot (x)$ 。

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

解题步骤 8

化简每一项。

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解题步骤 8.1

将

$\frac{\sin (x)}{\cos (x)}$ 转换成

$\tan (x)$ 。

$\frac{1}{\tan (x) + \frac{\cos (x)}{\sin (x)}} \cot (x)$

解题步骤 8.2

将

$\frac{\cos (x)}{\sin (x)}$ 转换成

$\cot (x)$ 。

$\frac{1}{\tan (x) + \cot (x)} \cot (x)$

解题步骤 9

组合

$\frac{1}{\tan (x) + \cot (x)}$ 和

$\cot (x)$ 。

$\frac{\cot (x)}{\tan (x) + \cot (x)}$

代数 示例

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