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 law, we get

Now consider the second part of the equation, we get

Substituting values from sine law, we get

Now consider the third part of the equation, we get

Substituting values from sine law, we get

From equation (i), (ii), and (iii), we get

Hence proved