Question

The value of ${\cos }^{-1}(-1/2)-2{\sin }^{-1}\left(1/2\right)+3{\cos }^{-1}(-1/\sqrt{2})-4{\tan }^{-1}(-1)$ is equal to-

• A. $7\pi /4$
• B. $11\pi /4$
• C. $43\pi /12$
• D. $25\pi /12$

Answer 1

Answer: (C)

$43\pi /12$

${\cos }^{-1}(-\frac{1}{2})-{\sin }^{-1}\left(\frac{1}{2}\right)+3{\cos }^{-1}(-\frac{1}{\sqrt{2}})-4{\tan }^{-1}(-1)$
$=\pi -{\cos }^{-1}(-\frac{1}{2})-2{\sin }^{-1}\left(\frac{1}{2}\right)+3[\pi -{\cos }^{-1}(-\frac{1}{\sqrt{2}})]+4{\tan }^{-1}(-1)$
$=\pi -\frac{\pi }{3}-\frac{2\pi }{6}+3(\pi -\frac{\pi }{4})+\frac{4\pi }{4}=\frac{43\pi }{12}$