If sinh (2 tanh ^{-1} x) = frac{11}{60},then | vedclass

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(C) Given,$\sinh (2 	anh ^{-1} x) = \frac{11}{60}$.Using the identity $\sinh (2 	heta) = \frac{2 	anh 	heta}{1 - 	anh ^2 	heta}$,where $	heta =

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$\frac{1}{11}$

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(C) Given,$\sinh (2 	anh ^{-1} x) = \frac{11}{60}$.Using the identity $\sinh (2 	heta) = \frac{2 	anh 	heta}{1 - 	anh ^2 	heta}$,where $	heta = 	anh ^{-1} x$,we have $	anh 	heta = x$.Substituting this into the equation:$\frac{2x}{1 - x^2} = \frac{11}{60}$$120x = 11(1 - x^2)$$11x^2 + 120x - 11 = 0$$11x^2 + 121x - x - 11 = 0$$11x(x + 11) - 1(x + 11) = 0$$(11x - 1)(x + 11) = 0$Thus,$x = \frac{1}{11}$ or $x = -11$.Since the domain of $	anh ^{-1} x$ is $(-1, 1)$,$x = -11$ is rejected.Therefore,$x = \frac{1}{11}$.

If $\sinh (2 \tanh ^{-1} x) = \frac{11}{60}$,then $x =$

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