Question

If the value of ${\tan }^{-1}\left(\tan \frac{3\pi }{4}\right)$ is $-\frac{\pi }{k},$ then $k$ is

Answer 1

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

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

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

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