f（x）=1／2cos^2x+根号3sinxcosx+3／2sin^2x 怎么化简

题目

f（x）=1／2cos^2x+根号3sinxcosx+3／2sin^2x 怎么化简

答案

f(x)=1/2(cos²x+2√3cosxsinx+3sin²x)
=1/2(cosx+√3sinx)²
=1/2[2sin(x+π/6)]²
=2sin²(x+π/6)