已知函数f(x)=2sinxcosx-2cosx^2+1.

1、
f(x)=sin2x-cos2x
=√2(√2/2*sin2x-√2/2cos2x)
=√2(sin2xcosπ/4-cos2xsinπ/4)
=√2sin(2x-π/4)
所以2x+π/4=2kπ+π/2,sin最大=1
2x+π/4=2kπ-π/2,sin最小=-1
所以
x=kπ+π/8,最大值=√2
x=kπ-3π/8,最小值=-√2
2、
f(θ)=sin2θ-cos2θ=3/5
平方
sin²2θ+cos²2θ-2sin2θcos2θ=9/25
1-sin4θ=9/25
sin4θ=16/25
原式=cos(π/2-4θ)
=sin4θ
=16/25

f(x)=2sinxcosx-2cosx^2+1;
2sinxcosx=sin2x;2cosx^2=1+cos2x;
f(x)=sin2x-cos2x.当x=3π/8;最大=根号2；