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