Question

Prove that : a sin A – b sin B = c sin (A – B).

Answer 1

 LHS = a sin A – b sin B

= k sin A.sin A – k sin B. sin B

= k [sin²A – sin²B]

= k [sin (A + B) sin (A – B)]

= k [sin (180° - C) sin (A – B)]

= k [sin C sin (A – B)]

= ksin C sin (A – B)

= c.sin (A – B) = RHS

∴ LHS = RHS