函数f(x)=sin(pai/2+x)cos(pai/6-x)的最大值

问题描述:

函数f(x)=sin(pai/2+x)cos(pai/6-x)的最大值

f(x)=sin(π/2+x)cos(π/6-x)
=cosxcos(π/6-x)
=cosx(1/2cosx+√3/2sinx)
=1/2cos^2x+√3/2sinxcosx
=1/4+1/4cos2x+√3/4sin2x
=1/2(1/2cos2x+√3/2sin2x)+1/4
=1/2sin(2x+π/6)+1/4
最大值=1/2+1/4=3/4