f(sin x)=3-cos 2x求f(cos x)

f(sin x)=3-cos 2x求f(cos x)
f(sin x)=3-cos 2x求f(cos x)

f(sin x)=3-cos 2x求f(cos x)
f(sinx)=3-cos2x=3-[1-2(sinx)^2]=2+2(sinx)^2
得到f(x)=2+2x^2
将cosx代入得f(cos x)=2+2cosx^2 =2+cos（2x）+1=3+cos（2x）

用π/2-x去换x有
f(sin(π/2- x))= 3-cos 2(π/2- x) 即= 3-cos(π- 2x) =3+cos2x
f(cosx)=3+cos2x

f(sinx)=3-cos2x=3-（cos²x-sin²x）=2+2sin²x。所以，f(cosx)=2+2cos²x

f(sinx)=3-cos2x=3-[1-2(sinx)^2]=2+2(sinx)^2
所以：f(x)=2+2x^2