Question:
If $\tan ^{-1}(\cot \theta)=2 \theta$, then $\theta=$ _________________.
Solution:
$\tan ^{-1}(\cot \theta)=2 \theta$
$\Rightarrow \tan ^{-1}\left[\tan \left(\frac{\pi}{2}-\theta\right)\right]=2 \theta$
$\Rightarrow \frac{\pi}{2}-\theta=2 \theta$
$\Rightarrow 3 \theta=\frac{\pi}{2}$
$\Rightarrow \theta=\frac{\pi}{6}$
Thus, the value of $\theta$ is $\frac{\pi}{6}$.
If $\tan ^{-1}(\cot \theta)=2 \theta$, then $\theta=\frac{\pi}{6}$
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