If cos θ = 35 and cos ϕ = 45, where θ and ϕ are
positive acute angles, then cos θ−ϕ2 =
75√2
We have cos θ = 35 and cos ϕ = 45.
Therefore cos(θ−ϕ)=cosθcosϕ+sinθsinϕ
= 35 . 45 + 45 . 35 = 2425
But 2cos2(θ−ϕ2)=1+cos(θ−ϕ) = 1 + 2425 = 4950
∴ cos2(θ−ϕ2) = 4950. Hence, cos(θ−ϕ2) = 75√2.