(1)f(x)=sinxcosx+cos^2x
=1/2sin2x+1/2(2cos^2x-1)+1/2
=1/2(sin2x+cos2x)+1/2
=(根号2)/2sin(2x+π/4)+1/2
T=2π/2=π
2x+π/4∈(-π/2+2kπ,π/2+2kπ)
2x∈(-3π/4+2kπ,π/4+2kπ)
x∈(-3π/8+kπ,π/8+kπ)
递增区间(-3π/8+kπ,π/8+kπ) ∈z
(2)
(根号2)/2sin(2x+π/4)+1/2=1/2
sin(2x+π/4)=0
2x+π/4=π
x=3π/8