Question

If sin (θ + 34°) = cos θ and θ is acute, then θ = ?
(a) 56°
(b) 66°
(c) 28°
(d) 42°

Answer 1

(d) 42°

$$\begin{gathered} \text{We have:} \\ \sin (\theta +{34}^0)=\cos \theta \\ =>\sin (\theta +{34}^0)=\sin ({90}^0-\theta )[\because \cos \theta =\sin ({90}^0-\theta )] \\ =>\theta +{34}^0={90}^0-\theta \\ =>2\theta ={56}^0 \\ \therefore \theta ={28}^0 \end{gathered}$$