三角学示例

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

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

解题步骤 1

将

1

$1$ 重写为

1^{2}

$1^{2}$ 。

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

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

解题步骤 2

将

(cos (x) + sin (x)) (cos (x) + sin (x))

$(\cos (x) + \sin (x)) (\cos (x) + \sin (x))$ 重写为

{(cos (x) + sin (x))}^{2}

${(\cos (x) + \sin (x))}^{2}$ 。

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

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

解题步骤 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)

$a^{2} - b^{2} = (a + b) (a - b)$ 进行因式分解，其中

a = 1

$a = 1$ 和

b = cos (x) + sin (x)

$b = \cos (x) + \sin (x)$ 。

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

解题步骤 4

运用分配律。

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

三角学 示例