Question : If $\sin (\theta+30°)=\cos 5 \theta$, then what is the value of $\theta$?
Option 1: 30°
Option 2: 10°
Option 3: 15°
Option 4: 20°
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Correct Answer: 10°
Solution :
Given,
$\sin (\theta+30°)=\cos 5 \theta$
We know, $\sin\theta=\cos(90°-\theta)$
⇒ $\sin (\theta+30°)=\sin(90°-5\theta)$
⇒ $\theta+30°=90°-5\theta$
⇒ $6\theta=60°$
⇒ $\theta=10°$
Hence, the correct answer is 10°.
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