f(x)=sin^2 (x+π/4)
a+b=sin^2 (lg5+π/4)+sin^2 (lg(1/5)+π/4)
=1-(cos(2lg5+π/2)+cos(2lg(1/5)+π/2))/2
=1+(sin(2lg5)+sin(2lg(1/5)))/2
=1+sin(lg5+lg(1/5))*cos(lg5-lg(1/5))
=1+0
=1