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Question

If sin (θ + 34°) = cos θ and θ + 34° is acute, find θ.
(a) 56°
(b) 28°
(c) 17°
(d) 14°

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Solution

(b) 28°
sin (θ + 34°) = cos θ
⇒ sin (θ + 34°) = cos (90° - θ) [ Since cos θ = sin (90° - θ)]
⇒ (θ + 34°) = (90° - θ)
⇒ 2θ = 56°
⇒ θ = 562=28°

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