Differentiate the function cos^{-1}(sin x) wi | vedclass

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(A) Let $y = \cos^{-1}(\sin x)$.We know that $\sin x = \cos(\frac{\pi}{2} - x)$.Substituting this into the expression,we get $y = \cos^{-1}(\cos(\frac

Vedclass · Accepted Answer

-$1$

Vedclass · Answer

(A) Let $y = \cos^{-1}(\sin x)$.We know that $\sin x = \cos(\frac{\pi}{2} - x)$.Substituting this into the expression,we get $y = \cos^{-1}(\cos(\frac{\pi}{2} - x))$.Since $\cos^{-1}(\cos 	heta) = 	heta$ for $	heta \in [0, \pi]$,we have $y = \frac{\pi}{2} - x$.Now,differentiating $y$ with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(\frac{\pi}{2} - x) = 0 - 1 = -1$.Thus,the derivative is $-1$.

Differentiate the function $\cos^{-1}(\sin x)$ with respect to $x$.

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