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

So the LHS of the given equation, we get

Substituting values from sine rule, we get

As A + B + C = π

Hence,

Similarly,

And,

Now , so the above equation becomes,

Canceling the like terms we get

Hence proved