Question

Find the principal value $cot^{-1} (1)$

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{2}$
• D. $0$

Answer 1

Answer: (B)

$\frac{\pi}{4}$

Answer 2

Let $cot^{-1} \left(1\right) = \theta$ $\Rightarrow\,cot\,\theta = 1$ $= cot \frac{\pi}{4}$ $\Rightarrow\,\theta = \frac{\pi}{4} \in (0$, $\pi)$ $\therefore$ Principal value of $cot^{-1} \left(1\right)$ is $\frac{\pi }{4}$