已知函数f(x)=2a cos^2 x+b sin x cos x-根号3/2,且f(0)=根号3/2,f(兀/4)=1/2

由f(0)=√3/2,f(π/4)=1/2,有a=√3/2,b=1
从而f(x)=√3cos^2 x+sin x cos x-√3/2
=√3cos^2 x+（1/2）sin2x-√3/2
=(√3/2)cos2x+（1/2）sin2x
=sin(2x+π/3)
1,T=π
2,2kπ+π/2≤2x+π/3≤2kπ+3π/2从中解得x