Question

If θ lies in the first quadrant and cos θ = 8/17, then find the value of cos (30° + θ) + cos (45° – θ) + cos (120° – θ).

Answer 1

Answer:

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Answer 2

Answer:

According to the question

cos θ = 8/17 sin θ = ±√(1 – cos2θ)

Since, θ lies in first quadrant, only positive sign can be 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 siny

Therefore,

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

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

nxt step in attachment

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