Question

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

Answer 1

解：
sin(α-360°)-cos(180°-α)=m
sina+cosa=m....(1)
sin^2a+cos^2a=1..(2)
(1)^2-(2)有2sinacosa=m^2-1
sinacosa=(m^2-1)/2
sin(180°+α)·cos(180°-α)
=-sina*(-cosa)
=sinacosa
= (m^2-1)/2

Answer 2

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