若f(sinx)=3-cos2x,则f(cosx)=( )A.3-cos2x B.3-sin2x C.3+cos2x D.3+sin2x

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 14:15:33

若f(sinx)=3-cos2x,则f(cosx)=( )A.3-cos2x B.3-sin2x C.3+cos2x D.3+sin2x
若f(sinx)=3-cos2x,则f(cosx)=( )
A.3-cos2x B.3-sin2x C.3+cos2x D.3+sin2x

若f(sinx)=3-cos2x,则f(cosx)=( )A.3-cos2x B.3-sin2x C.3+cos2x D.3+sin2x
f(sinx)
=3-cos2x
=3-[1-2(sinx)^2]
=2+2(sinx)^2
所以 f(x)=2+2x^2
当取值cosx时,
f(cosx)
=2+2(cosx)^2
=2+(1+cos2x)
=3+cos2x
答案选C

换x为x+π/2
f(sin(x+π/2))=3-cos2(x+π/2)
由sin(x+π/2)=cosx cos2(x+π/2)=cos(2x+π)=-cos2x
推出f(cosx)=3+cos2x
所以选C

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