三角学示例

\frac{cos (a - b)}{cos (a) cos (b)}

$\frac{\cos (a - b)}{\cos (a) \cos (b)}$

解题步骤 1

分离分数。

\frac{1}{cos (b)} \cdot \frac{cos (a - b)}{cos (a)}

$\frac{1}{\cos (b)} \cdot \frac{\cos (a - b)}{\cos (a)}$

解题步骤 2

将

\frac{cos (a - b)}{cos (a)}

$\frac{\cos (a - b)}{\cos (a)}$ 重写为乘积形式。

\frac{1}{cos (b)} (cos (a - b) \frac{1}{cos (a)})

$\frac{1}{\cos (b)} (\cos (a - b) \frac{1}{\cos (a)})$

解题步骤 3

将

cos (a - b)

$\cos (a - b)$ 写成分母为

1

$1$ 的分数。

\frac{1}{cos (b)} (\frac{cos (a - b)}{1} \cdot \frac{1}{cos (a)})

$\frac{1}{\cos (b)} (\frac{\cos (a - b)}{1} \cdot \frac{1}{\cos (a)})$

解题步骤 4

化简。

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解题步骤 4.1

用

cos (a - b)

$\cos (a - b)$ 除以

1

$1$ 。

\frac{1}{cos (b)} (cos (a - b) \frac{1}{cos (a)})

$\frac{1}{\cos (b)} (\cos (a - b) \frac{1}{\cos (a)})$

解题步骤 4.2

将

\frac{1}{cos (a)}

$\frac{1}{\cos (a)}$ 转换成

sec (a)

$\sec (a)$ 。

\frac{1}{cos (b)} (cos (a - b) sec (a))

$\frac{1}{\cos (b)} (\cos (a - b) \sec (a))$

\frac{1}{cos (b)} (cos (a - b) sec (a))

$\frac{1}{\cos (b)} (\cos (a - b) \sec (a))$

解题步骤 5

将

\frac{1}{cos (b)}

$\frac{1}{\cos (b)}$ 转换成

sec (b)

$\sec (b)$ 。

sec (b) (cos (a - b) sec (a))

$\sec (b) (\cos (a - b) \sec (a))$

解题步骤 6

使用两角差的公式

cos (x - y) = cos (x) cos (y) + sin (x) sin (y)

$\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ 。

sec (b) ((cos (a) cos (b) + sin (a) sin (b)) sec (a))

$\sec (b) ((\cos (a) \cos (b) + \sin (a) \sin (b)) \sec (a))$

解题步骤 7

通过相乘进行化简。

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解题步骤 7.1

运用分配律。

sec (b) (cos (a) cos (b) sec (a) + sin (a) sin (b) sec (a))

$\sec (b) (\cos (a) \cos (b) \sec (a) + \sin (a) \sin (b) \sec (a))$

解题步骤 7.2

运用分配律。

sec (b) cos (a) cos (b) sec (a) + sec (b) sin (a) sin (b) sec (a)

$\sec (b) \cos (a) \cos (b) \sec (a) + \sec (b) \sin (a) \sin (b) \sec (a)$

sec (b) cos (a) cos (b) sec (a) + sec (b) sin (a) sin (b) sec (a)

$\sec (b) \cos (a) \cos (b) \sec (a) + \sec (b) \sin (a) \sin (b) \sec (a)$

三角学 示例