已知函数f(x)=根号3cos^2x-根号3sin^2+2sinxcosx化简

题目

已知函数f(x)=根号3cos^2x-根号3sin^2+2sinxcosx化简

答案

f(x) = √3(cos²x - sin²x) + sin2x = √3cos2x + sin2x
= 2[(1/2)sin2x + (√3/2)cos2x]
= 2[sin2xcos(π/3) + cos2xsin(π/3)]
= 2sin(2x + π/3)