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受欢迎的三角函数 >

证明 3cos^2(x)-2=1-3sin^2(x)

解答

证明

3 cos^{2} (x) - 2 = 1 - 3 sin^{2} (x)

解答

真

求解步骤

3 cos^{2} (x) - 2 = 1 - 3 sin^{2} (x)

调整左侧

3 cos^{2} (x) - 2

使用三角恒等式改写

3 cos^{2} (x) - 2

使用毕达哥拉斯恒等式:

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

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

= 3 (1 - sin^{2} (x)) - 2

化简

3 (1 - sin^{2} (x)) - 2 : - 3 sin^{2} (x) + 1

3 (1 - sin^{2} (x)) - 2

乘开

3 (1 - sin^{2} (x)) : 3 - 3 sin^{2} (x)

3 (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 3, b = 1, c = sin^{2} (x)

= 3 \cdot 1 - 3 sin^{2} (x)

数字相乘:

3 \cdot 1 = 3

= 3 - 3 sin^{2} (x)

= 3 - 3 sin^{2} (x) - 2

化简

3 - 3 sin^{2} (x) - 2 : - 3 sin^{2} (x) + 1

3 - 3 sin^{2} (x) - 2

对同类项分组

= - 3 sin^{2} (x) + 3 - 2

数字相加/相减:

3 - 2 = 1

= - 3 sin^{2} (x) + 1

= - 3 sin^{2} (x) + 1

= - 3 sin^{2} (x) + 1

= - 3 sin^{2} (x) + 1

= 1 - 3 sin^{2} (x)

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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