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设F(sinx)=Cos2x+1,求F(Cosx)

供参考。

f(sinx)=cos2x+1 = 1-2sin²x+1 = 2 - 2sin²x 所以,f(x)=2-2x² 所以,f(cosx)=2-2cos²x=2sin²x

换元法

f(sinx)=1-cos2x=2(sin x)^2, 既有f(x)=2x^2, 故f(cos x)=2*(cos x)^2=1+cos2x.

待续

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