Question

The principal value of ${\tan }^{-1}\left(\cot \frac{3\pi }{4}\right)$ is :

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

Answer 1

The correct option is C $-\frac{\pi }{4}$

We have ${\tan }^{-1}(\cot \frac{3\pi }{4})$

$={\tan }^{-1}(\cot (\frac{\pi }{2}+\frac{\pi }{4}))$

$={\tan }^{-1}(-\tan \frac{\pi }{4})$

$={\tan }^{-1}\left(\tan \right(-\frac{\pi }{4}))$

$=-\frac{\pi }{4}$