# Prove the following identities:  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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