Prove the following identities:(cos α + cos β)2 + (sin α + sin β)2 = 4 cos2

Proof:Take LHS:{∵ cos (A – B) = cos A cos B + sin A sin B}{∵ cos2x = 2cos2 x – 1}= RHSHence Proved

Q11 of 123 Page 9

Prove the following identities:
(cos α + cos β)² + (sin α + sin β)² = 4 cos²

Proof:

Take LHS:

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

{∵ cos2x = 2cos² x – 1}

= RHS

Hence Proved

Prove the following identities:

1 + cos² 2x = 2(cos⁴ x + sin⁴ x)