
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 1st, 2018, 08:29 AM  #1 
Member Joined: Jul 2018 From: Germany Posts: 37 Thanks: 1  Cancelling sums in fractions
Help me do the impossible, I'm looking at this: $\displaystyle \frac{\sin(a+e)}{b}*\frac{u*\sin(e)  v*\sin(e)}{\sin(a)*\cos(e+a)+(1\cos(a))*\cos(e+a)}\frac{\cos(e+a)}{b}*\frac{u*\sin(e)  v*\cos(e)}{\sin(a)*\sin(a+e) + (1\cos(a))*\cos(a+e)} $ As you can see, both sides of the subtraction are very similar, I need to reduce 3 of these subtractions, if you have any hints on how to shorten the formulas, I'd be thankful. I'm almost certain that the outcome should be very simple actually, these formulas are part of a bigger one that describes interferencepatterns: Last edited by skipjack; October 1st, 2018 at 02:57 PM. 
October 1st, 2018, 01:15 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,786 Thanks: 708 
"Both sides of the subtraction"?? I suggest you check for typos.

October 1st, 2018, 02:16 PM  #3 
Member Joined: Jul 2018 From: Germany Posts: 37 Thanks: 1  
October 1st, 2018, 02:34 PM  #4 
Member Joined: Jul 2018 From: Germany Posts: 37 Thanks: 1 
And I did make some progress: $\displaystyle \frac{(1\cos(a))*\cos(a+e)}{\sin(a)}=\cos(a+e)*(\csc(a)\cot(a)) $ and I'm trying to simplify this atm: $\displaystyle \frac{(u*\sin(e)v*\cos(e))*\cos(a+e)}{\sin(a)} $ I think it has to do something with the golden ratio, as I tried visualizing it I saw that the graph peaks when $\displaystyle e=phi=0.618...$, that's at least pretty interesting to me. the rectangle represents $\displaystyle \sin(e)*\cos(e+a)$ and the line that goes Y represents $\displaystyle \frac{\sin(e)*\cos(e+a)}{\sin(a)}$ Last edited by skipjack; October 1st, 2018 at 03:00 PM. 

Tags 
cancelling, cosine, fractions, sine, sums 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cancelling differentials  photogo01  Calculus  30  January 16th, 2017 08:28 AM 
Justification for cancelling terms in limits?  Mr Davis 97  Calculus  7  August 14th, 2015 12:58 PM 
How to justify the cancelling of variables in a rational expression?  Mr Davis 97  Calculus  3  February 19th, 2015 05:16 AM 
Cancelling factors.  zengjinlian  Probability and Statistics  2  April 4th, 2014 02:35 PM 
Simplifying fractions with variables in fractions  nova3421  Algebra  1  September 9th, 2009 10:03 AM 