The value of $ an ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}} ight)+\cos ^{-1}\left(\frac{-1}{2} ight)$ is

Question

The value of $	an ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}ight)+\cos ^{-1}\left(\frac{-1}{2}ight)$ is

Aicharya · Accepted Answer

$\begin{aligned} & 	an ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}ight)+\cos ^{-1}\left(-\frac{1}{2}ight) \ & =-	an ^{-1}(\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}ight)+\pi-\cos ^{-1}\left(\frac{1}{2}ight) \ & =-\frac{\pi}{3}-\frac{\pi}{4}+\pi-\frac{\pi}{3}=\frac{\pi}{12}\end{aligned}$

The value of $\tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos…

Solution