If 2 cos left(2 tan ^{-1} xright)=1,then x= | vedclass

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(B) Given the equation $2 \cos \left(2 	an ^{-1} xight)=1$. Dividing by $2$,we get $\cos \left(2 	an ^{-1} xight) = \frac{1}{2}$. We know that $

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$\frac{1}{\sqrt{3}}$

Vedclass · Answer

(B) Given the equation $2 \cos \left(2 	an ^{-1} xight)=1$. Dividing by $2$,we get $\cos \left(2 	an ^{-1} xight) = \frac{1}{2}$. We know that $\cos 	heta = \frac{1}{2}$ when $	heta = \frac{\pi}{3}$. Therefore,$2 	an ^{-1} x = \frac{\pi}{3}$. Dividing by $2$,we get $	an ^{-1} x = \frac{\pi}{6}$. Taking the tangent of both sides,$x = 	an \left(\frac{\pi}{6}ight)$. Since $	an \left(\frac{\pi}{6}ight) = \frac{1}{\sqrt{3}}$,we have $x = \frac{1}{\sqrt{3}}$. Thus,the correct option is $B$.

If $2 \cos \left(2 \tan ^{-1} x\right)=1$,then $x=$ . . . . . .

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