已知sin(α+π/3)+sinα=-4√3/5,-π/2＜α＜0,求cosα的值不会的别胡说

Question

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

Answer 1

sin(α+π/3)+sinα=sinαcos(π/3)+cosαsin(π/3)+sinα=(1/2)sinα+(√3/2)cosα+sinα=(3/2)sinα+(√3/2)cosα=-4√3/5
则(√3/2)sinα+(1/2)cosα=-4/5
且sinα^2+cosα^2=1 另又-π/2＜α＜0,则sinα<0,cosα>0
由以上条件联立解得cosα=(3√3-4)/10