Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

The principal value of $\cot ^{-1}(-1)$ is

A. $\frac{-\pi}{4}$

B. $\frac{\pi}{4}$

C. $\frac{5 \pi}{4}$

D. $\frac{3 \pi}{4}$ 

Solution:

To Find: The Principle value of $\cot ^{-1}(-1)$

Let the principle value be given by $x$

Now, let $x=\cot ^{-1}(-1)$

$\Rightarrow \cot x=-1$

$\Rightarrow \cot x=-\cot \left(\frac{\pi}{4}\right)\left(\because \cot \left(\frac{\pi}{4}\right)=1\right)$

$\Rightarrow \cot x=\cot \left(\pi-\frac{\pi}{4}\right)(\because-\cot (\theta)=\cot (\pi-\theta))$

$\Rightarrow x=\frac{3 \pi}{4}$

 

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now