Question

The value of ${\tan }^{-1}\left(\cot \frac{43\pi }{4}\right)$ 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 $-\frac{\pi }{4}$

${\tan }^{-1}\left(\cot \frac{43\pi }{4}\right)={\tan }^{-1}\left[\cot (10\pi +\frac{3\pi }{4})\right]={\tan }^{-1}\left[\cot \left(\frac{3\pi }{4}\right)\right]={\tan }^{-1}(-\tan \frac{\pi }{4})={\tan }^{-1}\left[\tan (-\frac{\pi }{4})\right]=-\frac{\pi }{4}(\because {\tan }^{-1}\left(\tan x\right)=x,x\in (-\frac{\pi }{2},\frac{\pi }{2}))$