Question

If sin 3θ = cos (θ – 2°) where 3θ and (θ – 2°) are acute angles, what is the value of θ?

(a) 22° 

(b) 23° 

(c) 24° 

(d) 25°

Answer 1

(b) 23°

sin 3θ = cos (θ – 2°) 

⇒ cos (90° – 3θ ) = cos (θ – 2°) 

⇒ 90° – 3θ = θ – 2° 

⇒ 4θ = 92° ⇒ θ = 23°.