Question

If sin 3θ and (θ − 2°), where 3θ and (θ − 2°) are both acute angles, then θ = ?
(a) 44°
(b) 22°
(c) 46°
(d) 23°

Answer 1

(d) 23°
Disclaimer: In the question instead of [sin 3θ and (θ − 2°)] it should be [sin 3θ = cos (θ − 2°)]

sin 3θ = cos (θ − 2°)
⇒ cos (90° - 3θ) = cos (θ − 2°) [ Since cos ( 90° - θ) = sin θ]
⇒ (90° - 3θ) = (θ − 2°)
⇒ 92° = 4θ
⇒ θ = $\frac{92}{4}=23°$