If 4 cos^{-1} x + sin^{-1} x = frac{pi}{2},th | vedclass

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

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(A) We are given the equation: $4 \cos^{-1} x + \sin^{-1} x = \frac{\pi}{2}$.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:$4 \cos^{-1} x + (\frac{\pi}{2} - \cos^{-1} x) = \frac{\pi}{2}$.Simplifying the expression:$3 \cos^{-1} x + \frac{\pi}{2} = \frac{\pi}{2}$.Subtracting $\frac{\pi}{2}$ from both sides:$3 \cos^{-1} x = 0$.Dividing by $3$:$\cos^{-1} x = 0$.Taking the cosine of both sides:$x = \cos(0) = 1$.

If $4 \cos^{-1} x + \sin^{-1} x = \frac{\pi}{2}$,then $x =$ . . . . . . .

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