If 2 operatorname{Tanh}^{-1} x = operatorname | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $2 \operatorname{Tanh}^{-1} x = \operatorname{Sinh}^{-1}\left(\frac{4}{3}ight)$.Let $\operatorname{Tanh}^{-1} x = 	heta$, then $x = 	anh

Vedclass · Accepted Answer

$\log (2+\sqrt{3})$

Vedclass · Answer

(C) Given $2 \operatorname{Tanh}^{-1} x = \operatorname{Sinh}^{-1}\left(\frac{4}{3}ight)$.Let $\operatorname{Tanh}^{-1} x = 	heta$, then $x = 	anh 	heta$.So, $2	heta = \operatorname{Sinh}^{-1}\left(\frac{4}{3}ight)$, which implies $\sinh(2	heta) = \frac{4}{3}$.Using the identity $\sinh(2	heta) = \frac{2	anh 	heta}{1-	anh^2 	heta}$, we have $\frac{2x}{1-x^2} = \frac{4}{3}$.$6x = 4 - 4x^2 \implies 4x^2 + 6x - 4 = 0 \implies 2x^2 + 3x - 2 = 0$.Solving for $x$: $(2x-1)(x+2) = 0$. Since $|x| Now, we need to find $\operatorname{Cosh}^{-1}\left(\frac{1}{x}ight) = \operatorname{Cosh}^{-1}(2)$.Using the formula $\operatorname{Cosh}^{-1} y = \log(y + \sqrt{y^2-1})$, we get $\operatorname{Cosh}^{-1}(2) = \log(2 + \sqrt{2^2-1}) = \log(2 + \sqrt{3})$.

If $2 \operatorname{Tanh}^{-1} x = \operatorname{Sinh}^{-1}\left(\frac{4}{3}\right)$, then $\operatorname{Cosh}^{-1}\left(\frac{1}{x}\right) = $

Similar Questions

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

The value of $\tan \left\{\frac{1}{2} \sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\frac{1}{2} \cos ^{-1}\left(\frac{1-y^2}{1+y^2}\right)\right\}$ is

Suppose $S_a(x) = \operatorname{Sec}^{-1}\left(\frac{x}{a}\right) + \operatorname{Sec}^{-1}(a)$ for $a \neq 0$. If $S_a(x) = S_b(x)$ for $a \neq b$,then $x =$

If $\tan^{-1} \frac{a+x}{a} + \tan^{-1} \frac{a-x}{a} = \frac{\pi}{6}$,then $x^2 =$

$\sin \left\{ {{\sin }^{ - 1}}\frac{1}{2} + {{\cos }^{ - 1}}\frac{1}{2} \right\} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module