If 5 sinh x - cosh x = 5,then one of the valu | vedclass

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

Question

(C) Given $5 \sinh x - \cosh x = 5$. Rearranging,we get $5 \sinh x - 5 = \cosh x$,which implies $5(\sinh x - 1) = \cosh x$. Squaring both sides,we hav

Vedclass · Accepted Answer

$\frac{-3}{5}$

Vedclass · Answer

(C) Given $5 \sinh x - \cosh x = 5$. Rearranging,we get $5 \sinh x - 5 = \cosh x$,which implies $5(\sinh x - 1) = \cosh x$. Squaring both sides,we have $25(\sinh^2 x + 1 - 2 \sinh x) = \cosh^2 x$. Using the identity $\cosh^2 x - \sinh^2 x = 1$,we substitute $\cosh^2 x = 1 + \sinh^2 x$: $25 \sinh^2 x + 25 - 50 \sinh x = 1 + \sinh^2 x$. $24 \sinh^2 x - 50 \sinh x + 24 = 0$. Dividing by $2$,we get $12 \sinh^2 x - 25 \sinh x + 12 = 0$. Factoring the quadratic: $(3 \sinh x - 4)(4 \sinh x - 3) = 0$. Thus,$\sinh x = \frac{4}{3}$ or $\sinh x = \frac{3}{4}$. If $\sinh x = \frac{4}{3}$,then $\cosh x = 5(\frac{4}{3} - 1) = \frac{5}{3}$,so $	anh x = \frac{\sinh x}{\cosh x} = \frac{4/3}{5/3} = \frac{4}{5}$. If $\sinh x = \frac{3}{4}$,then $\cosh x = 5(\frac{3}{4} - 1) = -\frac{5}{4}$,so $	anh x = \frac{\sinh x}{\cosh x} = \frac{3/4}{-5/4} = -\frac{3}{5}$. Therefore,one of the values is $-\frac{3}{5}$.

If $5 \sinh x - \cosh x = 5$,then one of the values of $\tanh x$ is

Similar Questions

If $\sin x \cosh y = \cos \theta$,$\cos x \sinh y = \sin \theta$ and $4 \tan x = 3$,then $\sinh^2 y =$

$\cos 12^{\circ} + \cos 60^{\circ} + \cos 84^{\circ} + \cos 132^{\circ} + \cos 156^{\circ} = $

If $\cos \theta - 4 \sin \theta = 1$,then $\sin \theta + 4 \cos \theta$ is equal to

If $\frac{1 - \cos x}{\cos x(1 + \cos x)} = \frac{\sin \alpha}{\cos x} - \frac{2}{1 + \cos x}$,then $\alpha = $

If $\cosh x = \operatorname{cosec} \theta$,then $\coth^2 \frac{x}{2} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module