求y=sin(x-π/3)sinx最大值

问题描述:

求y=sin(x-π/3)sinx最大值

y=(sinxcosπ/3-cosxsinπ/3)sinx=(1/2*sinx-√3/2*cosx)sinx=1/2*sin²x-√3/2*sinxcosx=1/2*(1-cos2x)/2-√3/4*sin2x=-1/2*(sin2x*√3/2+cos2x*1/2)+1/4=-1/2*(sin2xcosπ/6+cos2xsinπ/6)+1/4=-1/2*sin(2x+π...