Answer :


Proof:


Take LHS:



Identities used:


cos 2x = cos2 x – sin2 x


sin 2x = 2 sin x cos x


Therefore,




{ a2 – b2 = (a - b)(a + b) & sin2 x + cos2 x = 1}



{ a2 + b2 + 2ab = (a + b)2}




Multiplying numerator and denominator by







{ sin (A – B) = sin A cos B – sin B cos A


cos (A – B) = cos A cos B + sin A sin B}




= RHS


Hence Proved


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