题目

化简一个函数.f(x)=-1/2+sin(π/6-2x)+cos(2x-π/3)+(cosx)^2

提问时间：2021-01-14

答案

化简f(x)=-1/2+sin(π/6-2x)+cos(2x-π/3)+cos²x
y=-1/2-sin(2x-π/6)+cos(2x-π/3)+cos²x
=-1/2-[sin2xcos(π/6)-cos2xsin(π/6)]+cos2xcos(π/3)+sin2xsin(π/3)+cos²x
=-1/2-(√3/2)sin2x+(1/2)cos2x+(1/2)cos2x+(√3/2)sin2x+cos²x
=-1/2+cos2x+cos²x=-1/2+2cos²x-1+cos²x=3cos²x-3/2=(3/2)(2cos²x-1)=(3/2)cos2x.