(C) We know that $\tanh(y) = \frac{e^y - e^{-y}}{e^y + e^{-y}}$.Substituting $y = \log x$,we get:$\tanh(\log x) = \frac{e^{\log x} - e^{-\log x}}{e^{\

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

(C) We know that $\tanh(y) = \frac{e^y - e^{-y}}{e^y + e^{-y}}$.Substituting $y = \log x$,we get:$\tanh(\log x) = \frac{e^{\log x} - e^{-\log x}}{e^{\log x} + e^{-\log x}}$Since $e^{\log x} = x$ and $e^{-\log x} = e^{\log(x^{-1})} = \frac{1}{x}$,the expression becomes:$\tanh(\log x) = \frac{x - \frac{1}{x}}{x + \frac{1}{x}}$Multiplying the numerator and denominator by $x$,we get:$\tanh(\log x) = \frac{x^2 - 1}{x^2 + 1}$

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

Easy

$\tanh (\log x) = $

AP EAMCET 2022 All AP EAMCET

A
$\frac{x+1}{x-1}$
B
$\frac{x^2+1}{x^2-1}$
C
$\frac{x^2-1}{x^2+1}$
D
$2x$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

Previous Year

AP EAMCET 2022 Paper All AP EAMCET years →

Evaluate: $\sin ^2\frac{\pi }{8} + \sin ^2\frac{3\pi }{8} + \sin ^2\frac{5\pi }{8} + \sin ^2\frac{7\pi }{8} = $

Medium

View Solution

$\cos ^2 45^{\circ}+\cos ^2 135^{\circ}+\cos ^2 225^{\circ}+\cos ^2 315^{\circ} = $

EasyAP EAMCET 2022

View Solution

If $\tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$,then $\sin \alpha + \cos \alpha$ and $\sin \alpha - \cos \alpha$ are equal to:

Medium

View Solution

Which of the following is true?

View Solution

If $x = \tan 15^{\circ}$,$y = \operatorname{cosec} 75^{\circ}$ and $z = 4 \sin 18^{\circ}$,then :

DifficultTS EAMCET 2006

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$\tanh (\log x) = $

Similar Questions

Evaluate: $\sin ^2\frac{\pi }{8} + \sin ^2\frac{3\pi }{8} + \sin ^2\frac{5\pi }{8} + \sin ^2\frac{7\pi }{8} = $

$\cos ^2 45^{\circ}+\cos ^2 135^{\circ}+\cos ^2 225^{\circ}+\cos ^2 315^{\circ} = $

If $\tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$,then $\sin \alpha + \cos \alpha$ and $\sin \alpha - \cos \alpha$ are equal to:

Which of the following is true?

If $x = \tan 15^{\circ}$,$y = \operatorname{cosec} 75^{\circ}$ and $z = 4 \sin 18^{\circ}$,then :

Vedclass Test Series

Exam Paper Generator

Online Exam Module