If 4 sin ^{-1} x + cos ^{-1} x = pi,then x = | vedclass

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(C) We are given the equation $4 \sin ^{-1} x + \cos ^{-1} x = \pi$. We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2}$,which implies

Vedclass · Accepted Answer

$\frac{1}{2}$

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(C) We are given the equation $4 \sin ^{-1} x + \cos ^{-1} x = \pi$. We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2}$,which implies $\cos ^{-1} x = \frac{\pi}{2} - \sin ^{-1} x$. Substituting this into the given equation: $4 \sin ^{-1} x + (\frac{\pi}{2} - \sin ^{-1} x) = \pi$ $3 \sin ^{-1} x + \frac{\pi}{2} = \pi$ $3 \sin ^{-1} x = \frac{\pi}{2}$ $\sin ^{-1} x = \frac{\pi}{6}$ Taking the sine of both sides: $x = \sin(\frac{\pi}{6}) = \frac{1}{2}$. Thus,the correct option is $C$.

If $4 \sin ^{-1} x + \cos ^{-1} x = \pi$,then $x = $

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