Calculus Calculus Math Forum

 October 12th, 2015, 02:55 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. $\displaystyle cos(x)cos(x)=\frac{1}{2}*cos(x+x)+\frac{1}{2}*cos( x-x)$ 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  October 12th, 2015, 04:23 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 $cos(x)cos(y) ={1\over 4}(e^{ix} +e^{-ix})(e^{iy}+e^{-iy}) =$ ${1\over 4}(e^{i(x+y)} +e^{-i(x+y)}) + {1\over 4}(e^{i(x-y)}+ e^{-i(x-y)})$ $={1\over 2}(cos(x+y) + cos(x-y))$ October 18th, 2015, 09:31 AM #3 Senior Member   Joined: Dec 2014 From: Canada Posts: 110 Thanks: 4 Thanks explains a lot  Tags equation, euler, inverse Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post shreddinglicks Differential Equations 5 October 29th, 2014 04:15 PM muzialis Calculus 0 May 1st, 2012 11:18 AM FalkirkMathFan Calculus 1 November 5th, 2011 01:57 AM FalkirkMathFan Calculus 0 November 3rd, 2011 05:52 PM Tumbler Differential Equations 3 April 19th, 2011 08:57 AM

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