A community for students.
Here's the question you clicked on:
 0 viewing
baldymcgee6
 3 years ago
Show that sinh(3t)*sinh(t)=1+2cosh(2t) for t≠0
baldymcgee6
 3 years ago
Show that sinh(3t)*sinh(t)=1+2cosh(2t) for t≠0

This Question is Closed

baldymcgee6
 3 years ago
Best ResponseYou've already chosen the best response.0@LolWolf, @AccessDenied, @lgbasallote

baldymcgee6
 3 years ago
Best ResponseYou've already chosen the best response.0sinh(3t)/sinh(t)=1+2cosh(2t) for t≠0

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.0they aren't equal...try again

baldymcgee6
 3 years ago
Best ResponseYou've already chosen the best response.0@Algebraic! do you know how to do it?

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2\[ \text{sinh} \; x = \frac{e^x  e^{x}}{2} \] We can rewrite the lefthand side to match the righthand side. \[ \frac{e^{3x}  e^{3x}}{2} \div \frac{e^x  e^{x}}{2} \\ \frac{e^{3x}  e^{3x}}{\cancel{2}} \times \frac{\cancel{2}}{e^x  e^{x}}\\ \frac{e^{3x}  e^{3x}}{e^x  e^{x}} \\ \frac{(e^x)^3  (e^{x})^3}{e^x  e^{x}} \] If we consider the numerator as a difference of cubes, we can factor it like this: \( a^3  b^3 = (a  b)(a^2 + ab + b^2)\). Notice that this creates a factor in the denominator that is also in the numerator.

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2When the factors cancel, this remains: \[ \frac{\cancel{(e^x  e^{x})}((e^x)^2 + e^x e^{x} + (e^{x})^2)}{\cancel{e^x  e^{x}}} \\ = e^{2x} + 1 + e^{2x} \] Which starts to look a lot like 2cosh 2x + 1, it should be simple manipulation to justify that from there.

baldymcgee6
 3 years ago
Best ResponseYou've already chosen the best response.0@AccessDenied YOU ROCK, thanks so much!!

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2I should note that I am using x instead of t. My bad. :P

AccessDenied
 3 years ago
Best ResponseYou've already chosen the best response.2and, I'm glad to help! :)

baldymcgee6
 3 years ago
Best ResponseYou've already chosen the best response.0thanks so much again

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.0don't forget, you can redeem your medals for cash prizes at the end of every month.

LolWolf
 3 years ago
Best ResponseYou've already chosen the best response.1So we know: \[ \sinh x=\frac{e^xe^{x}}{2} \]Therefore: \[ \sinh 3x=\frac{e^{3x}e^{3x}}{2} \]So: \[ \frac{\sinh(3t)}{\sinh(t)}=\frac{2}{e^xe^{x}}\cdot\frac{e^{3x}e^{3x}}{2}=\frac{2e^x}{e^{2x}1}\cdot\frac{e^{6x}1}{2e^{3x}}=\\ \frac{2e^x}{e^{2x}1}\cdot\frac{e^{6x}1}{2e^{3x}}=\frac{(e^{2x}1)(e^{4x}+e^{2x}+1)}{e^{2x}(e^{2x}1)}=\\ \frac{e^{4x}+e^{2x}+1}{e^{2x}}=e^{2x}+1+e^{2x}=1+2\cosh x \]Ahh, this takes forever... and I mad a mistake halfway through, so I had to restart... anyways, +1 internets to @AccessDenied

baldymcgee6
 3 years ago
Best ResponseYou've already chosen the best response.0lol, thanks for you valiant effort @LolWolf

LolWolf
 3 years ago
Best ResponseYou've already chosen the best response.1Valiantly late, haha, but, yes
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.