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Please Solve R.D.Sharma Class 12 Chapter 3 Inverse Trigonometric Functions Exercise Multiple Choice Questions Question 30 Maths Textbbok Solution.

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Answer: \pm \frac{\pi}{6}

Hint: Try to solve \tan ^{-1} function and cot function.

Given: \tan ^{-1}(\cot \theta)=2 \theta


\tan ^{-1}(\cot \theta)=2 \theta

\tan 2 \theta=\cot \theta

\frac{2 \tan \theta}{1-\tan ^{2} \theta}=\frac{1}{\tan \theta}

2 \tan ^{2} \theta=1-\tan ^{2} \theta

\begin{aligned} &3 \tan ^{2} \theta=1 \\ &\tan ^{2} \theta=\frac{1}{3} \\ &\tan \theta=\pm \frac{1}{\sqrt{3}} \\ &\theta=\pm \frac{\pi}{6} \end{aligned}

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