x+y=60度 则sinx•siny最小值
3个回答

sinx siny

=sinx sin(60°-x)

=sinx【sin60°cosx-cos60°sinx】

=sinx【(√3/2)cosx-(1/2)sinx】

=(√3/2)sinxcosx-(1/2)sin²x

=(√3/4)sin2x - (1/4)(1-cos2x)

=(1/2)【(√3/2)sin2x+(1/2)cos2x】-(1/4)

=(1/2)(sin60°sin2x+cos60°cos2x)-(1/4)

=(1/2)cos(2x-60°)-(1/4)

最小值为:-3/4