If cos left(cos ^{-1} frac{sqrt{3}}{2}+sin ^{ | vedclass

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Question

(B) Given the equation: $\cos \left(\cos ^{-1} \frac{\sqrt{3}}{2}+\sin ^{-1} x\right)=1$ Taking $\cos ^{-1}$ on both sides: $\cos ^{-1} \frac{\sqrt{3}

Vedclass · Accepted Answer

$-\frac{1}{2}$

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(B) Given the equation: $\cos \left(\cos ^{-1} \frac{\sqrt{3}}{2}+\sin ^{-1} xight)=1$ Taking $\cos ^{-1}$ on both sides: $\cos ^{-1} \frac{\sqrt{3}}{2}+\sin ^{-1} x = \cos ^{-1}(1)$ We know that $\cos ^{-1}(1) = 0$ and $\cos ^{-1} \frac{\sqrt{3}}{2} = \frac{\pi}{6}$. Substituting these values: $\frac{\pi}{6} + \sin ^{-1} x = 0$ $\sin ^{-1} x = -\frac{\pi}{6}$ $x = \sin \left(-\frac{\pi}{6}ight)$ Since $\sin(-	heta) = -\sin(	heta)$,we have: $x = -\sin \left(\frac{\pi}{6}ight) = -\frac{1}{2}$ Thus,the value of $x$ is $-\frac{1}{2}$.

If $\cos \left(\cos ^{-1} \frac{\sqrt{3}}{2}+\sin ^{-1} x\right)=1$,then find the value of $x$.

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