The value of cos^{-1}(cos 12) - sin^{-1}(sin | vedclass

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(C) We know that $\cos^{-1}(\cos x) = x - 2n\pi$ if $x \in [2n\pi, (2n+1)\pi]$. For $x = 12$,since $3\pi \approx 9.42$ and $4\pi \approx 12.56$,we hav

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$8\pi - 26$

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(C) We know that $\cos^{-1}(\cos x) = x - 2n\pi$ if $x \in [2n\pi, (2n+1)\pi]$. For $x = 12$,since $3\pi \approx 9.42$ and $4\pi \approx 12.56$,we have $3\pi We know that $\sin^{-1}(\sin x) = x - 2n\pi$ if $x \in [2n\pi - \pi/2, 2n\pi + \pi/2]$. For $x = 14$,since $4\pi \approx 12.56$ and $4\pi + \pi/2 \approx 14.13$,we have $4\pi - \pi/2 Therefore,$\cos^{-1}(\cos 12) - \sin^{-1}(\sin 14) = (4\pi - 12) - (14 - 4\pi) = 8\pi - 26$.

The value of $\cos^{-1}(\cos 12) - \sin^{-1}(\sin 14)$ is

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