The value of cos^{-1}left(cosfrac{5pi}{3}righ | vedclass

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Question

(A) We know that for any $x \in [-1, 1]$,the identity $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ holds true.In the given expression,let $x = \cos\f

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$\frac{\pi}{2}$

Vedclass · Answer

(A) We know that for any $x \in [-1, 1]$,the identity $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ holds true.In the given expression,let $x = \cos\frac{5\pi}{3}$.Since $\cos\frac{5\pi}{3} = \cos(2\pi - \frac{\pi}{3}) = \cos\frac{\pi}{3} = \frac{1}{2}$,which lies in the interval $[-1, 1]$,we can apply the identity.Therefore,$\cos^{-1}\left(\cos\frac{5\pi}{3}\right) + \sin^{-1}\left(\cos\frac{5\pi}{3}\right) = \frac{\pi}{2}$.

The value of $\cos^{-1}\left(\cos\frac{5\pi}{3}\right) + \sin^{-1}\left(\cos\frac{5\pi}{3}\right)$ is

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