Question : If $\tan 2 \theta=\cot \left(\theta-36^{\circ}\right)$, where $2 \theta$ is an acute angle, then the value of $\theta$ is:
Option 1: 18°
Option 2: 36°
Option 3: 30°
Option 4: 42°
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Correct Answer: 42°
Solution :
Given, $\tan 2 \theta=\cot \left(\theta-36^{\circ}\right)$
⇒ $\tan 2 \theta=\tan \left(90^{\circ}-\theta+36^{\circ}\right)$
⇒ $2\theta=126^{\circ}-\theta$
⇒ $3\theta=126^{\circ}$
$\therefore \theta=42^{\circ}$
Hence, the correct answer is 42°.
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