$\cos^{- 1}\left( \frac{- 1}{2} ight) - 2\sin^{- 1}{\left( \frac{1}{2} ight) + 3\cos^{- 1}\left( \frac{- 1}{\sqrt{2}} ight)}\ \ - 4 an^{- 1}( - 1)$ equals

Question

$\cos^{- 1}\left( \frac{- 1}{2} ight) - 2\sin^{- 1}{\left( \frac{1}{2} ight) + 3\cos^{- 1}\left( \frac{- 1}{\sqrt{2}} ight)}\ \ - 4	an^{- 1}( - 1)$ equals

Dr. Abubacker · Accepted Answer

(d)
$\cos^{- 1}{\left( - \frac{1}{2} ight) - 2\sin^{- 1}\left( \frac{1}{2} ight) + 3\cos^{- 1}{\left( - \frac{1}{\sqrt{2}} ight) + 4	an^{- 1}{( - 1)}}}$
$\  = \pi - \cos^{- 1}{\left( \frac{1}{2} ight) - 2\left( \frac{\pi}{6} ight) + 3\left( \pi - \cos^{- 1}\left( \frac{1}{\sqrt{2}} ight) ight)}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  + 4	an^{- 1}{(1)}$
$= \pi - \frac{\pi}{3} - \frac{\pi}{3} + 3\left( \pi - \frac{\pi}{4} ight) + 4.\frac{\pi}{4}$
$\ \  = \frac{\pi}{3} + 3.\frac{3\pi}{4} + \pi = \frac{43\pi}{12}$

Q. $\cos^{- 1}\left( \frac{- 1}{2} \right) - 2\sin^{- 1}{\left( \frac{1}{2} \right) + 3\cos^{- 1}\left( \frac{- 1}{\sqrt{2}} \right)}\ \ - 4\tan^{- 1}( - 1)$ equals

Explanation

Reviewed by Dr. Abubacker

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