若sin(α-360°)-cos(180°-α)=m,则sin(180°+α)·cos(180°-α)等于

题目

若sin(α-360°)-cos(180°-α)=m,则sin(180°+α)·cos(180°-α)等于

答案

sin(α-360°)-cos(180°-α)=m
所以sinα+cosα=m
平方
sin²α+cos²α+2sinαcosα=m²
1+2sinαcosα=m²
sinαcosα=(m²-1)/2
sin(180°+α)·cos(180°-α)
=-sinα·(-cosα)
=(m²-1)/2