The value of cos ^{-1}left(cot left(frac{pi}{ | vedclass

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(A) We are given the expression $\cos ^{-1}\left(\cot \left(\frac{\pi}{2}\right)\right)+\cos ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$.Firs

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$\frac{2 \pi}{3}$

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(A) We are given the expression $\cos ^{-1}\left(\cot \left(\frac{\pi}{2}\right)\right)+\cos ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$.First,evaluate the inner trigonometric functions:$\cot \left(\frac{\pi}{2}\right) = 0$.$\sin \left(\frac{2 \pi}{3}\right) = \sin \left(\pi - \frac{\pi}{3}\right) = \sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$.Now,substitute these values back into the expression:$\cos ^{-1}(0) + \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$.We know that $\cos ^{-1}(0) = \frac{\pi}{2}$ and $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right) = \frac{\pi}{6}$.Adding these values gives:$\frac{\pi}{2} + \frac{\pi}{6} = \frac{3\pi + \pi}{6} = \frac{4\pi}{6} = \frac{2\pi}{3}$.

The value of $\cos ^{-1}\left(\cot \left(\frac{\pi}{2}\right)\right)+\cos ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$ is

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