若f(sinX)=3-cos2X,则f(cosX)为

若f(sinX)=3-cos2X,则f(cosX)为
A. 3- cos2X
B. 3- sin2X
C. 3+ cos2X
D. 3+ sin2X

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∵庆磨肢f(sinx)=3-cos2x=3-(1-2sinx*sinx)
∴f(x)=3-(1-2x*x)
=2+2x*x

或游粗者：设誉世sinx=t
cos2x=1-2(sinx)^2=1-2t^2
f(sinx)=3-cos2x
f(t)=3-(1-2t^2)=2t^2+2
把t改成x
f(x)=2x^2+2
f(cosx)=2cos^2 x+2=1+cos2x+2=3+cos2x

选C

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f(sinX)=3-cos2X
=3-[1-2(sinx)^2]
=2+2(sinx)^2
所悉培以 f(x)=2+2x^2
所以f(cosx)=2+2(cosx)^2
=3+[2(cosx)^2-1]
=3+cos2x
所配山以培陆中选C

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∵庆磨肢f(sinx)=3-cos2x=3-(1-2sinx*sinx)
∴f(x)=3-(1-2x*x)
=2+2x*x

或游粗者：设誉世sinx=t
cos2x=1-2(sinx)^2=1-2t^2
f(sinx)=3-cos2x
f(t)=3-(1-2t^2)=2t^2+2
把t改成x
f(x)=2x^2+2
f(cosx)=2cos^2 x+2=1+cos2x+2=3+cos2x

选C

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