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


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