Question

已知0＜β＜,＜α＜,cos(-α)=，sin(+β)=,求sin(α+β)的值.

Answer 1

思路分析：注意(+β)-(-α)=+(α+β),可通过求出+β和-α的正、余弦值来求sin(α+β).

解：∵＜α＜,∴-＜-α＜0.

∴sin(-α)=.

又∵0＜β＜,∴＜+β＜π.

∴cos(+β)=.

sin(α+β)=-cos(+α+β)=-cos［(+β)-(-α)］

=-cos(+β)cos(-α)-sin(+β)sin(-α)

=-(-)×-×（-）=.