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. $\frac{3 \pi}{4}$

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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. $\frac{3 \pi}{4}$

CBSE | Class 12 | Inverse Trigonometric Functions | Maths | RS Aggarwal

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:

Option(D) is correct.
To Find: The Principle value of $\cot ^{-1}(-1)$
Let the principle value be given by $x$
Now, let $x=\cot ^{-1}(-1)$
$\Rightarrow \cot x=-1$
$\Rightarrow \cot x=-\cot \left(\frac{\pi}{4}\right)\left(\because \cot \left(\frac{\pi}{4}\right)=1\right)$
$\Rightarrow \cot x=\cot \left(\pi-\frac{\pi}{4}\right)(\because-\cot (\theta)=\cot (\pi-\theta))$
$\Rightarrow x=\frac{3 \pi}{4}$