If cos α + cos β = a , sin α + sin β = b and α - β = 2 θ , then cos 3 θ cos θ is equal to

Step-by-step solution

cos 3 θ cos θ = 4 cos 2 θ - 3 = 2 1 + cos 2 θ - 3 = 2 cos 2 θ - 1 = 2 cos α - β - 1 Now, cos 2 α + sin 2 α + cos 2 β + sin 2 β + 2 cos α - β = a 2 + b 2 ⇒ 2 cos α - β = a 2 + b 2 - 2 ⇒ cos 3 θ cos θ = a 2 + b 2 - 3