(sinA+sinB)/(cos A +cos B) =tan (A+B)/2 怎么证明?

(sinA+sinB)/(cos A +cos B) =tan (A+B)/2 怎么证明?
(sinA+sinB)/(cos A +cos B) =tan (A+B)/2 怎么证明?

(sinA+sinB)/(cos A +cos B) =tan (A+B)/2 怎么证明?
(sinA+sinB)/(cos A +cos B)
=2sin(A+B)/2*cos(A-B)/cos2/cos(A+B)/2*cosA-B)/2
=sin(A+B)/2/cos(A+B)/2
=tan (A+B)/2
用和差化积公式

分式上下同时应用积化和差公式即可(参见必修4)