If 3 cos ^{-1} x + sin ^{-1} x = pi,then x = | vedclass

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Question

(A) We are given the equation $3 \cos ^{-1} x + \sin ^{-1} x = \pi$. We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2}$,which implies

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$\frac{1}{\sqrt{2}}$

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(A) We are given the equation $3 \cos ^{-1} x + \sin ^{-1} x = \pi$. We know the identity $\sin ^{-1} x + \cos ^{-1} x = \frac{\pi}{2}$,which implies $\sin ^{-1} x = \frac{\pi}{2} - \cos ^{-1} x$. Substituting this into the given equation: $3 \cos ^{-1} x + (\frac{\pi}{2} - \cos ^{-1} x) = \pi$ $2 \cos ^{-1} x + \frac{\pi}{2} = \pi$ $2 \cos ^{-1} x = \pi - \frac{\pi}{2}$ $2 \cos ^{-1} x = \frac{\pi}{2}$ $\cos ^{-1} x = \frac{\pi}{4}$ $x = \cos(\frac{\pi}{4})$ $x = \frac{1}{\sqrt{2}}$ Therefore,the correct option is $A$.

If $3 \cos ^{-1} x + \sin ^{-1} x = \pi$,then $x = $ . . . . . . .

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