Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

$\tan ^{-1}(-1)+\cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)=?$

A. $\frac{\pi}{2}$

B. $\pi$

C. $\frac{3 \pi}{2}$

D. $\frac{2 \pi}{3}$

 

Solution:

To Find: The value of $\tan ^{-1}(-1)+\cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)$

Let, $x=\tan ^{-1}(-1)+\cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)$

$\Rightarrow \mathrm{x}=-\tan ^{-1}(1)+\left(\pi-\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)\right)$

$\left(\because \tan ^{-1}(-\theta)=-\tan ^{-1}(\theta)\right.$ and $\left.\cos ^{-1}(-\theta)=\pi-\cos ^{-1}(\theta)\right)$

$\Rightarrow \mathrm{x}=-\frac{\pi}{4}+\left(\pi-\frac{\pi}{4}\right)$

$\Rightarrow \mathrm{x}=-\frac{\pi}{4}+\frac{3 \pi}{4}$

$\Rightarrow \mathrm{x}=\frac{\pi}{2}$

 

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