Question

Prove that : (sin A + sin B)/(sin A - sin B) = tan ((A+B)/2)cot((A-B)/2)

\(\frac{sin\,A\,+\,sin\,B}{sin\,A\,-\,sin\,B}\) = tan(\(\frac{A+B}{2}\))cot(\(\frac{A-B}{2}\))

Answer 1

(sin A + sin B)/(sin A - sin B) = tan ((A+B)/2)cot((A-B)/2)

Take L.H.S.:

\(\frac{sin\,A\,+\,sin\,B}{sin\,A\,-\,sin\,B}\)

= R.H.S. 

Hence Proved