Q. 7
Prove the following identities:
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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