Question

函数y=cos(x+60)cos(x+120)的最大值是

Answer 1

y=(cosxcos60-sinxsin60)(cosxcos120-sinxsin120)

=(1/2cosx-√3/2sinx)(-1/2cosx-√3/2sinx)

=-(1/2cosx-√3/2sinx)(1/2cosx+√3/2sinx)

=-1/4cos^2x+3/4sin^2x

=sin^2x-1/4(sin^2x+cos^2x)

=sin^2x-1/4

当sinx=1时,y取得最大值ymax=1^2-1/4=3/4