Question

The expression $$ \sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\sec ^{-1}(-\sqrt{2})+\tan ^{-1}(-1)+\operatorname{cosec}^{-1}(-\sqrt{2})+\cos ^{-1}\left(-\frac{1}{2}\right)+\tan ^{-1}(1-\sqrt{2})+\cot ^{-1}(\sqrt{2}+1) $$ simplifies to

• A. $\pi$
• B. $ \frac{7 \pi}{6}$
• C. 0
• D. $\frac{\pi}{2}$

Answer 1

Answer: (B)

$\frac{\pi}{4}+\frac{3 \pi}{4}-\frac{\pi}{4}-\frac{\pi}{4}+\frac{2 \pi}{3}-\frac{\pi}{8}+\frac{\pi}{8}=\frac{7 \pi}{6}$