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受欢迎的三角函数 >

证明 2sin^2(x)-1=1-2cos^2(x)

解答

证明

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

解答

真

求解步骤

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

调整左侧

2 sin^{2} (x) - 1

使用三角恒等式改写

2 sin^{2} (x) - 1

使用毕达哥拉斯恒等式:

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

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

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

化简

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

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

乘开

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

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

使用分配律:

a (b - c) = ab - a c

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

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

数字相乘:

2 \cdot 1 = 2

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

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

化简

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

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

对同类项分组

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

数字相加/相减:

2 - 1 = 1

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

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

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

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

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

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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