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
Similarly, b = k sin B
And c = k sin C…..(i)
So, a - b = k(sin A - sin B)..(ii)
So the given LHS becomes,
Substituting equation (i) and (ii) in the above equation, we get
Applying half angle rule,
And
Substituting equation (iii) and (iv) in equation (ii), we get
But
And
So the above equations in equation (v), we get
Dividing numerator and denominator by, we get
By canceling the like terms we get,
Hence proved