f(x)=(1+1/tanx)sin(x)^2
=sin(x)^2+sin(x)^2/tanx
=sin(x)^2+sin(x)cos(x)
=(1-cos(2x))/2+sin(2x)/2
=(sin(2x)-cos(2x))/2+1/2
=√2sin(2x-45°)/2+1/2