Question

已知函数f(x)=根号3（sin^2x-cos^2x）+2sinxcosx+a的最大值是3

Answer 1

f(x)=根号3（sin^2x-cos^2x）+2sinxcosx+a

=sin2x-根号3cos2x+a

=2(1/2sing2x-根号3/2cos2x)+a

=2sin(2x-π/6)+a

故a=3

最小值为-2+a=1

最小正周期为π