If sinh x = frac{12}{5},then sinh 3x + cosh 3 | vedclass

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

Question

(A) We know that $\sinh x = \frac{e^x - e^{-x}}{2}$ and $\cosh x = \frac{e^x + e^{-x}}{2}$.Given $\sinh x = \frac{12}{5}$,we have $\frac{e^x - e^{-x}}

Vedclass · Accepted Answer

$125$

Vedclass · Answer

(A) We know that $\sinh x = \frac{e^x - e^{-x}}{2}$ and $\cosh x = \frac{e^x + e^{-x}}{2}$.Given $\sinh x = \frac{12}{5}$,we have $\frac{e^x - e^{-x}}{2} = \frac{12}{5}$,which implies $e^x - e^{-x} = \frac{24}{5}$.Let $e^x = t$. Then $t - \frac{1}{t} = \frac{24}{5}$.Multiplying by $5t$,we get $5t^2 - 24t - 5 = 0$.Factoring the quadratic equation: $(5t + 1)(t - 5) = 0$.Since $e^x = t$ must be positive,$t = 5$,so $e^x = 5$.We need to find $\sinh 3x + \cosh 3x$.Using the definitions,$\sinh 3x + \cosh 3x = \frac{e^{3x} - e^{-3x}}{2} + \frac{e^{3x} + e^{-3x}}{2} = e^{3x}$.Since $e^x = 5$,$e^{3x} = (e^x)^3 = 5^3 = 125$.

If $\sinh x = \frac{12}{5}$,then $\sinh 3x + \cosh 3x = $

Similar Questions

The smallest positive value (in degrees) of $\theta$ for which $\tan(\theta+100^{\circ})=\tan(\theta+50^{\circ}) \tan(\theta) \tan(\theta-50^{\circ})$ is valid,is (in $^{\circ}$)

If $\sum_{r=1}^{50} \tan ^{-1} \frac{1}{2 r^{2}}=p$,then the value of $\tan p$ is :

If $2y \cos \theta = x \sin \theta$ and $2x \sec \theta - y \csc \theta = 3$,then $x^2 + 4y^2 = $

If $\cos^3 80^{\circ} + \cos^3 40^{\circ} - \cos^3 20^{\circ} = k$,then $\frac{4k}{3} =$

For $0 \leq x \leq \pi$,if $81^{\sin ^2 x}+81^{\cos ^2 x}=30$,then $x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module