三角学示例

{cos}^{2} (x) - {sin}^{2} (x) = 1 - 2 {sin}^{2} (x)

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

解题步骤 1

将所有表达式移到等式左边。

点击获取更多步骤...

解题步骤 1.1

从等式两边同时减去

1

$1$ 。

{cos}^{2} (x) - {sin}^{2} (x) - 1 = - 2 {sin}^{2} (x)

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

解题步骤 1.2

在等式两边都加上

2 {sin}^{2} (x)

$2 \sin^{2} (x)$ 。

{cos}^{2} (x) - {sin}^{2} (x) - 1 + 2 {sin}^{2} (x) = 0

$\cos^{2} (x) - \sin^{2} (x) - 1 + 2 \sin^{2} (x) = 0$

{cos}^{2} (x) - {sin}^{2} (x) - 1 + 2 {sin}^{2} (x) = 0

$\cos^{2} (x) - \sin^{2} (x) - 1 + 2 \sin^{2} (x) = 0$

解题步骤 2

化简

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

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

点击获取更多步骤...

解题步骤 2.1

移动

- 1

$- 1$ 。

{cos}^{2} (x) - 1 - {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$\cos^{2} (x) - 1 - \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.2

将

{cos}^{2} (x)

$\cos^{2} (x)$ 和

- 1

$- 1$ 重新排序。

- 1 + {cos}^{2} (x) - {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$- 1 + \cos^{2} (x) - \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.3

将

- 1

$- 1$ 重写为

- 1 (1)

$- 1 (1)$ 。

- 1 (1) + {cos}^{2} (x) - {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$- 1 (1) + \cos^{2} (x) - \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.4

从

{cos}^{2} (x)

$\cos^{2} (x)$ 中分解出因数

- 1

$- 1$ 。

- 1 (1) - 1 (- {cos}^{2} (x)) - {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$- 1 (1) - 1 (- \cos^{2} (x)) - \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.5

从

- 1 (1) - 1 (- {cos}^{2} (x))

$- 1 (1) - 1 (- \cos^{2} (x))$ 中分解出因数

- 1

$- 1$ 。

- 1 (1 - {cos}^{2} (x)) - {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$- 1 (1 - \cos^{2} (x)) - \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.6

将

- 1 (1 - {cos}^{2} (x))

$- 1 (1 - \cos^{2} (x))$ 重写为

- (1 - {cos}^{2} (x))

$- (1 - \cos^{2} (x))$ 。

- (1 - {cos}^{2} (x)) - {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$- (1 - \cos^{2} (x)) - \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.7

使用勾股恒等式。

- {sin}^{2} (x) - {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$- \sin^{2} (x) - \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.8

从

- {sin}^{2} (x)

$- \sin^{2} (x)$ 中减去

{sin}^{2} (x)

$\sin^{2} (x)$ 。

- 2 {sin}^{2} (x) + 2 {sin}^{2} (x) = 0

$- 2 \sin^{2} (x) + 2 \sin^{2} (x) = 0$

解题步骤 2.9

将

- 2 {sin}^{2} (x)

$- 2 \sin^{2} (x)$ 和

2 {sin}^{2} (x)

$2 \sin^{2} (x)$ 相加。

0 = 0

$0 = 0$

0 = 0

$0 = 0$

解题步骤 3

因为

0 = 0

$0 = 0$ ，所以方程对于

x

$x$ 的所有值将恒成立。

所有实数

解题步骤 4

结果可以多种形式表示。

所有实数

区间计数法：

(- \infty, \infty)

$(- \infty, \infty)$

三角学 示例

三角学示例