f(x)=(sinx+cosx)^2-2cos^2x=1--2cos^2x+2sinxcosx=sin2x-cosx=√2sin(2x-π/4)
f(x)最小正周期T=π
f(-π/12)=-√2sin(5π/12)<0
f(π/6)=)=√2sin(π/12)>0
所以f(-π/12)<(π/6)