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

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(B) Given equation is $2\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{2}.$Dividing both sides by $2,$ we get $\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{

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(B) Given equation is $2\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{2}.$Dividing both sides by $2,$ we get $\cos^{-1}\sqrt{\frac{1+x}{2}} = \frac{\pi}{4}.$Taking cosine on both sides,we have $\sqrt{\frac{1+x}{2}} = \cos\left(\frac{\pi}{4}\right).$Since $\cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}},$ we get $\sqrt{\frac{1+x}{2}} = \frac{1}{\sqrt{2}}.$Squaring both sides,$\frac{1+x}{2} = \frac{1}{2}.$Multiplying by $2,$ we get $1+x = 1,$which implies $x = 0.$

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

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