f(x) =1+cos2x+根号3sin2x+a怎么化简得f(x) =2sin(2x+π/6 )+a+1

题目

f(x) =1+cos2x+根号3sin2x+a怎么化简得f(x) =2sin(2x+π/6 )+a+1
三角函数我还没学,才学到向量.

答案

f(x) =1+cos2x+√3sin2x+a
=1+2[(1/2)*cos2x+(√3/2)sin2x]+a
因为sin(π/6)=1/2,cos(π/6)=√3/2,根据两角和正弦公式,sin(A+B)=sinAcosB+cosAsinB
f(x) =1+2sin(2x+π/6 )+a