sin^2a+cos^2(π/6+a)+1/2sin(2a+π/6)

题目

sin^2a+cos^2(π/6+a)+1/2sin(2a+π/6)

答案

=(1-cos2a)/2+(1+cos(π/3+2a))/2+1/2sin(2a+π/6)
=1-1/2cos2a+1/4cos2a-√3/4sin2a+√2/4sin2a+1/4cos2a （利用公式展开）
=1