My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Thanks Tree4Thanks
  • 1 Post By bigyan1einstein
  • 3 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
April 18th, 2016, 08:20 PM   #1
Senior Member
 
Joined: Apr 2008

Posts: 193
Thanks: 3

a horrible looking trigonometric identity

I am really stuck in the identity below.

Prove



Using sums and differences, I can simplify the terms with





Next, putting these results in the expression on the left side gives



I don't know what to do now. Could someone please help me? Thank you very much.

Last edited by skipjack; April 18th, 2016 at 11:51 PM.
davedave is offline  
 
April 18th, 2016, 08:36 PM   #2
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,815
Thanks: 1458

Go to the link ... Look at #1, (a) and (c)

Sum and Product of sine and cosine
skeeter is offline  
April 18th, 2016, 11:20 PM   #3
Member
 
Joined: Mar 2016
From: Nepal

Posts: 37
Thanks: 4

(cosA-cosB)/(sinB-sinA)
=(-2.sin(A+B/2).sin(A-B/2))/((2cosB+A/2.sinB-A/2)) [This is the product form of sin and cos for differences of different angles]
upon cancelling terms by adjusting signs you get
(sin(A+B/2))/(cosA+B/2))
=tan(A+B/2)
Thank me.
Thanks from Pacioli
bigyan1einstein is offline  
April 19th, 2016, 12:46 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 20,262
Thanks: 1958

More parentheses would be needed; it's clearer if formatted neatly.

$\displaystyle \frac{\cos A - \cos B}{\sin B - \sin A} = \frac{-2\sin{\small\dfrac{A+B}{2}} \sin{\small\dfrac{A-B}{2}}}{2\cos{\small\dfrac{B+A}{2}} \sin{\small\dfrac{B-A}{2}}} = \frac{\sin{\small\dfrac{A+B}{2}}} {\cos{\small\dfrac{A+B}{2}}} = \tan\frac{A+B}{2}$
Thanks from fysmat, Pacioli and evs
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
horrible, identity, trigonometric



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Trigonometric identity Lobinho Trigonometry 7 March 31st, 2015 03:13 PM
Another trigonometric identity #2 OriaG Trigonometry 2 August 13th, 2012 04:35 PM
Another trigonometric identity OriaG Trigonometry 10 August 12th, 2012 05:37 PM
Help on trigonometric identity chnixi Algebra 1 August 19th, 2009 04:52 AM
trigonometric identity TG Algebra 2 March 7th, 2008 04:22 PM





Copyright © 2019 My Math Forum. All rights reserved.