If 3 sin ^{-1}left(frac{2 x}{1+x^2}right)-4 c | vedclass

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(C) Let $x = 	an 	heta$,where $	heta \in (-\frac{\pi}{2}, \frac{\pi}{2})$.Then the given expression becomes:$3 \sin ^{-1}(\sin 2	heta) - 4 \cos ^{

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

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(C) Let $x = 	an 	heta$,where $	heta \in (-\frac{\pi}{2}, \frac{\pi}{2})$.Then the given expression becomes:$3 \sin ^{-1}(\sin 2	heta) - 4 \cos ^{-1}(\cos 2	heta) + 2 	an ^{-1}(	an 2	heta) = \frac{\pi}{3}$.Assuming $x \in (-1, 1)$,then $2	heta \in (-\frac{\pi}{2}, \frac{\pi}{2})$.Thus,$3(2	heta) - 4(2	heta) + 2(2	heta) = \frac{\pi}{3}$.$6	heta - 8	heta + 4	heta = \frac{\pi}{3}$.$2	heta = \frac{\pi}{3} \implies 	heta = \frac{\pi}{6}$.Therefore,$x = 	an(\frac{\pi}{6}) = \frac{1}{\sqrt{3}}$.

If $3 \sin ^{-1}\left(\frac{2 x}{1+x^2}\right)-4 \cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)+2 \tan ^{-1}\left(\frac{2 x}{1-x^2}\right)=\frac{\pi}{3}$,then the value of $x=$

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