Question

The principal value of $ta{n}^{-1}\left(cot\frac{43\pi }{4}\right)$ is :

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

Answer 1

Answer: (C)

${\tan }^{-1}[\cot (11\pi -\pi /4)]$
$={\tan }^{-1}[-\cot \pi /4]$
$=-{\tan }^{-1}(\cot \pi /4)$
$=-{\tan }^{-1}(1)$
$=-\pi /4$