f(x)=(sinx+cosx)^2-2sin^2x
=sinx^2+cos^2+2sinxcosx-2sin^2x
=cos^2x-sin^2x+sin2x
=cos2x+sin2x
=√2sin(π/4+2x)
单调递减区间
2Kπ+π/2≤π/4+2x≤(2K+1)π+π/2
2Kπ+π/4≤2x≤2Kπ+5π/4
Kπ+π/8≤x≤Kπ+5π/8
f(x)=(sinx+cosx)^2-2sin^2x
=sinx^2+cos^2+2sinxcosx-2sin^2x
=cos^2x-sin^2x+sin2x
=cos2x+sin2x
=√2sin(π/4+2x)
单调递减区间
2Kπ+π/2≤π/4+2x≤(2K+1)π+π/2
2Kπ+π/4≤2x≤2Kπ+5π/4
Kπ+π/8≤x≤Kπ+5π/8