Question

The value of ${\tan }^{-1}\left\{\tan \left(\frac{3\pi }{5}\right)\right\}$ is

• A. $\frac{3\pi }{5}$
• B. $\frac{-3\pi }{5}$
• C. $\frac{2\pi }{5}$
• D. $\frac{-2\pi }{5}$

Answer 1

Answer: (D)

We have, ${\tan }^{-1}\left\{\tan \left(\frac{3\pi }{5}\right)\right\}$
$={\tan }^{-1}\left\{\tan \left(\pi -\frac{2\pi }{5}\right)\right\}={\tan }^{-1}\left\{\tan \left(\frac{-2\pi }{5}\right)\right\}$
$=\frac{-2\pi }{5}\left[\because {\tan }^{-1}(\tan x)=x,x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)\right]$