If tan−1 (cot $\theta$) = 2 $\theta$, then $\theta$ =

Question

KollegeApply · Accepted Answer

(c) +-pi/6 \text{We have}, \tan^{- 1} \left( cot$\theta$ \right) = 2$\theta$ \Rightarrow \tan2$\theta$ = cot$\theta$ \Rightarrow \frac{2\tan$\theta$}{1 - \tan^2 $\theta$} = 1/\tan$\theta$ \Rightarrow 2 \tan^2 $\theta$ = 1 - \tan^2 $\theta$ \Rightarrow 3 \tan^2 $\theta$ = 1 \Rightarrow \tan^2 $\theta$ = $\frac{1}{3}$ \Rightarrow \tan$\theta$ = $\pm$ 1/$\sqrt$(3) \therefore $\theta$ = $\pm$ $\pi$/6

AChoose Your Answer