求函数f(x)=(sinx+cosx)^2+2cos^2x的单调增区间

问题描述:

求函数f(x)=(sinx+cosx)^2+2cos^2x的单调增区间

f(x)=(sinx+cosx)^2+2cos^2x
=2sinxcosx+1+2cos^2x
=2sinxcosx+1+1+cos2x
=sin2x+cos2x+2
=√2sin(2x+π/4)+2
则-π/2+2kπ