(2-sin(x)^2)-(2-cos(x)^2)＝cos2x 如何证明啊?

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(2-sin(x)^2)-(2-cos(x)^2)＝cos2x 如何证明啊?
(2-sin(x)^2)-(2-cos(x)^2)＝cos2x 如何证明啊?

(2-sin(x)^2)-(2-cos(x)^2)＝cos2x 如何证明啊?
(2-sin(x)^2)-(2-cos(x)^2)
=2-sin(x)^2-2+cos(x)^2
=cos(x)^2-sin(x)^2
=cos2x

去掉括号则cos(x)^2-sin(x)^2=cos2x

(2-sin(x)^2)-(2-cos(x)^2)=cos^2 x-sin^2 x=cos2x

左边=-(sinx)^2+(cosx)^2=1-(sinx)^2+(cosx)^2-1=2(cosx)^2-1=cos2x


公式：cos2x=cosx^2-sinx^2
(2-sin(x)^2)-(2-cos(x)^2)=cosx^2-sinx^2
所以(2-sin(x)^2)-(2-cos(x)^2)＝cos2x

∵cos2x=cosxcosx-sinxsinx=cos²x-sin²x
∴左边=cos²x-sin²x=cos2x=右边

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