f(x)=cos²x-sin²x+2√3sinxcosx+1 =cos2x+√3sin2x+1 =2sin(2x+π/6)+1f(a)=22sin(2x+π/6)+1=2sin(2x+π/6)=1/22x+π/6=π/6+2kπx=kπ2x+π/6=5π/6+2kπ2x=2π/3+2kπx=π/3+kπ∵α∈[π/4,π/2]∴a=π/3
