My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 12th, 2015, 01:55 PM   #1
Senior Member
 
BonaviaFx's Avatar
 
Joined: Dec 2014
From: Canada

Posts: 110
Thanks: 4

Inverse Euler's Equation

I am suppose to use Euler's equations to prove the following.

let x represent theta in this case.

$\displaystyle cos(x)cos(x)=\frac{1}{2}*cos(x+x)+\frac{1}{2}*cos( x-x) $

Would I start from the left hand side? Because I substituted cos(x) with Euler's equation and multiplied with the other cos(x). But didn't seem to be making sense.

Any help would be appreciated
BonaviaFx is offline  
 
October 12th, 2015, 03:23 PM   #2
Newbie
 
Joined: Oct 2015
From: Toronto

Posts: 14
Thanks: 1

The euler equation says:

$cos(x) = {1\over 2}(e^{ix} +e^{-ix})$

This implies
$cos(x)cos(y) ={1\over 4}(e^{ix} +e^{-ix})(e^{iy}+e^{-iy}) =$

${1\over 4}(e^{i(x+y)} +e^{-i(x+y)}) + {1\over 4}(e^{i(x-y)}+ e^{-i(x-y)})$

$={1\over 2}(cos(x+y) + cos(x-y))$
Aristide Tsemo is offline  
October 18th, 2015, 08:31 AM   #3
Senior Member
 
BonaviaFx's Avatar
 
Joined: Dec 2014
From: Canada

Posts: 110
Thanks: 4

Thanks explains a lot
BonaviaFx is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
equation, euler, inverse



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
How do you solve this Cauchy-Euler equation? shreddinglicks Differential Equations 5 October 29th, 2014 03:15 PM
Euler Lagrange Equation Computation muzialis Calculus 0 May 1st, 2012 10:18 AM
Euler method/ Euler formula FalkirkMathFan Calculus 1 November 5th, 2011 12:57 AM
Euler method/ Euler formula FalkirkMathFan Calculus 0 November 3rd, 2011 04:52 PM
Solve second order differential equation(Euler's method) Tumbler Differential Equations 3 April 19th, 2011 07:57 AM





Copyright © 2019 My Math Forum. All rights reserved.