Hyperbolic Identities - need help

Feb 2018
3
0
UK
Im kinda working ahead of myself on my assignment and I am stuck on this question:

Solve the following for X

cosh^2(x) + 5sinh(x) + 6 = 1 + sinh^2 (x)

Any help would be great!

 

Plato

MHF Helper
Aug 2006
22,475
8,643
Im kinda working ahead of myself on my assignment and I am stuck on this question:

Solve the following for X

cosh^2(x) + 5sinh(x) + 6 = 1 + sinh^2 (x)
Because $\cosh^2(x)=1+\sinh^2(x)$ you really have just
$5\sinh(x)+6=0\\\sinh(x)=\dfrac{-6}{5}$

What can you do now?
 
  • Like
Reactions: 1 person
Feb 2018
3
0
UK
Thanks Plato that was a massive help! I knew nothing about hyperbola so I went on to read a bit more after looking at your reply and came up with this which I hope is correct!

(cosh^2(x)-sinh^2(x)0+5sinh(x)=1-6

Using identity (cosh^2(x)-sinh^2(x))=1

1+5 sinh(x) = -5
5sinh(x) = -5-1
5 sinh(x) = -6
sinh(x)=-6/5
sinh(x)=-1.2
sinh^-1(-1.2)=x

x = -1.015973134