In any triangle ABC, prove the following:
Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get
⇒ a = k sin A, b = k sin B, c = k sin C
Here we will consider LHS, so we get
Substituting corresponding values from sine rule in the above equation, we get
Canceling the like terms, we get
But sin(A - B) = sin A cos B – cos A sin B, so the above equation becomes
Cancelling the like terms, we get,
LHS = 0 = RHS
Hence proved