Question

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

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

Answer 1

Answer: (B)

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