Answer :

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


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