MCQ
If $\tan ^{-1}(\cot \theta)=2 \theta$, then $\theta$ is equal to
- A$\frac{\pi}{3}$
- B$\frac{\pi}{4}$
- C$\frac{\pi}{6}$
- DNone of these
✓
Answer
$
\begin{array}{l}
\text { (c) }: \tan ^{-1}(\cot \theta)=2 \theta \Rightarrow \cot \theta=\tan 2 \theta \\
\Rightarrow \cot \theta=\cot \left(\frac{\pi}{2}-2 \theta\right) \Rightarrow \theta=\frac{\pi}{2}-2 \theta \\
\Rightarrow \quad 3 \theta=\frac{\pi}{2} \Rightarrow \theta=\frac{\pi}{6}
\end{array}
$
\begin{array}{l}
\text { (c) }: \tan ^{-1}(\cot \theta)=2 \theta \Rightarrow \cot \theta=\tan 2 \theta \\
\Rightarrow \cot \theta=\cot \left(\frac{\pi}{2}-2 \theta\right) \Rightarrow \theta=\frac{\pi}{2}-2 \theta \\
\Rightarrow \quad 3 \theta=\frac{\pi}{2} \Rightarrow \theta=\frac{\pi}{6}
\end{array}
$
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