October 12th, 2015, 01:55 PM  #1 
Senior Member 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( xx) $ 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 
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 $cos(x)cos(y) ={1\over 4}(e^{ix} +e^{ix})(e^{iy}+e^{iy}) =$ ${1\over 4}(e^{i(x+y)} +e^{i(x+y)}) + {1\over 4}(e^{i(xy)}+ e^{i(xy)})$ $={1\over 2}(cos(x+y) + cos(xy))$ 
October 18th, 2015, 08:31 AM  #3 
Senior Member Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 
Thanks explains a lot 

Tags 
equation, euler, inverse 
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