Question

If tan⁻¹(cotθ) = 2θ, then θ = __________________.

Answer 1

$$\begin{gathered} {\tan }^{-1}\left(\cot \theta \right)=2\theta \\ \Rightarrow {\tan }^{-1}\left[\tan \left(\frac{\mathrm{\pi }}{2}-\theta \right)\right]=2\theta \\ \Rightarrow \frac{\mathrm{\pi }}{2}-\theta =2\theta \\ \Rightarrow 3\theta =\frac{\mathrm{\pi }}{2} \\ \Rightarrow \theta =\frac{\mathrm{\pi }}{6} \end{gathered}$$

Thus, the value of $\theta$ is $\frac{\mathrm{\pi }}{6}$.

If tan⁻¹(cotθ) = 2θ, then θ = $\underline{\frac{\mathrm{\pi }}{6}}$.