Question

$\tan {}^{-1}\left(\tan 3\pi /4\right)=$

• A. $5\pi /4$
• B. $\pi /4$
• C. $-\pi /4$
• D. None of these

Answer 1

Answer: (A), (B)

The correct options are
A $5\pi /4$
B $\pi /4$

Let $y={\tan }^{-1}\left(\tan \frac{3\pi }{4}\right)$

$\Rightarrow \tan y=\tan (\pi -\frac{\pi }{4})$

$\Rightarrow \tan y=\tan \frac{\pi }{4}$

$\therefore y=\frac{\pi }{4},\pi +\frac{\pi }{4}$

$\Rightarrow y=\frac{\pi }{4},\frac{4\pi +\pi }{4}$

$\therefore y=\frac{\pi }{4},\frac{5\pi }{4}$