Question

已知sin（α＋π/3）+sinα=-4√3/5，-π/2<α<0,求cosα的值

Answer 1

-π<a<0
则sina>0
原式化简
sina*cosπ/3+cosa*sinπ/3+sina=-4√3/5
即3/2sina+√3/2cosa=-4√3/5
两边同除√3得
√3/2sina+1/2cosa=-4/5
sin(a+π/6）=-4/5
然后你自己用计算器搞把！！！

Answer 2

(3/2)sina+(√3/2)cosa=-4√3/5
(√3/2)sina+(1/2)cosa=-4/5
sin(a+π/6)=-4/5
cos(a+π/6)=3/5
cosa=cos(a+π/6)cos(π/6)+sin(a+π/6)sin(π/6)
=(3/5)(√3/2)+(-4/5)(1/2)
=(3√3-4)/10