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(D) We use the properties of inverse trigonometric functions: $\cos^{-1}(-x) = \pi - \cos^{-1}(x)$, $\sin^{-1}(-x) = -\sin^{-1}(x)$, and $	an^{-1}(-x

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$\frac{43 \pi}{12}$

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(D) We use the properties of inverse trigonometric functions: $\cos^{-1}(-x) = \pi - \cos^{-1}(x)$, $\sin^{-1}(-x) = -\sin^{-1}(x)$, and $	an^{-1}(-x) = -	an^{-1}(x)$.Given expression: $E = \cos^{-1}\left(-\frac{1}{2}ight) - 2\sin^{-1}\left(\frac{1}{2}ight) + 3\cos^{-1}\left(-\frac{1}{\sqrt{2}}ight) - 4	an^{-1}(-1)$Step $1$: Apply the properties:$E = \left(\pi - \cos^{-1}\left(\frac{1}{2}ight)ight) - 2\left(\frac{\pi}{6}ight) + 3\left(\pi - \cos^{-1}\left(\frac{1}{\sqrt{2}}ight)ight) - 4\left(-\frac{\pi}{4}ight)$Step $2$: Substitute the standard values:$E = \left(\pi - \frac{\pi}{3}ight) - \frac{\pi}{3} + 3\left(\pi - \frac{\pi}{4}ight) + \pi$Step $3$: Simplify the expression:$E = \frac{2\pi}{3} - \frac{\pi}{3} + 3\left(\frac{3\pi}{4}ight) + \pi$$E = \frac{\pi}{3} + \frac{9\pi}{4} + \pi$$E = \frac{4\pi + 27\pi + 12\pi}{12} = \frac{43\pi}{12}$

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

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