# 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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