If θ lies in the first quadrant and then find the value of cos(30° + θ) + cos (45° – θ) + cos (120° – θ)

Given,

cos θ = 8/17

∴ sin θ = ±√(1 – cos²θ)

But θ lies in first quadrant, so only positive sign is considered.

⇒ sin θ = √( 1 – 64/289) = 15/17

Let, y = cos(30° + θ) + cos (45° – θ) + cos (120° – θ)

We know that: cos(x + y) = cos x cos y – sin x sin y

∴ y = cos30° cos θ – sin30° sin θ + cos45° cos θ + sin45°sin θ +cos120° cos θ + sin120° sin θ

Putting values of cos30° ,sin30° ,cos 120° ,sin120° and cos 45°