Question

$\cot {}^{-1}\left(\cot 5\pi /4\right)=$

• A. $\pi /4$
• B. $-\pi /4$
• C. $3\pi /4$
• D. none of these

Answer 1

Answer: (A)

$\pi /4$

Let $y={\cot }^{-1}\left(\cot \frac{5\pi }{4}\right)$

$\Rightarrow \cot y=\cot (\pi +\frac{\pi }{4})$

$\Rightarrow \cot y=\cot \frac{\pi }{4}$ since $\pi +\theta$ is in third quadrant,$\cot (\pi +\frac{\pi }{4})$ is positive.

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