已知函数f(x)=1+cos2x-2sin^2(x-30°).化简

问题描述:

已知函数f(x)=1+cos2x-2sin^2(x-30°).化简

f(x)=1+cos2x-2sin^2(x-30°).=cos2x+cos2(x-30)=cos2x+sin(2x+30)=cos2x+sin2xcos30+cos2xsin30=(3cos2x)/2+(√3sin2x)/2=√3(sin60cos2x+cos60sin2x)=√3sin(2x+60)