?
Solved

Problem with Trig Identity

Posted on 2014-11-17
10
Medium Priority
?
140 Views
Last Modified: 2014-11-17
Hi,

I can't seem to prove the following trig identity, or where to start. Any ideas?

Thanks!
TrigIdentity.jpg
0
Comment
Question by:Computer Guy
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 6
  • 4
10 Comments
 
LVL 27

Expert Comment

by:d-glitch
ID: 40447347
Start by replacing tan and cot with their sin and cos equivalents.  
This should be  a four line proof.
0
 
LVL 3

Author Comment

by:Computer Guy
ID: 40447484
So  1+sin/cos would = cos * sin/cos
0
 
LVL 27

Expert Comment

by:d-glitch
ID: 40447519
>>  So  1+sin/cos would = cos * sin/cos

That is not true, nor one of the steps.

You have to methodically transform the Left-Hand-Side of the equation until it matches the right.

Half of the first step is to replace   1 + tan    with    1 + sin/cos
0
Technology Partners: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 
LVL 3

Author Comment

by:Computer Guy
ID: 40447542
Woops, that part I knew.

I mean to say that

(cos/1)/(1+(sin/cos)) where the 1's and the cos cancel out left with sinx for the first part, right?
0
 
LVL 27

Expert Comment

by:d-glitch
ID: 40447573
After the first step, you will still have two terms on the LHS

One of them will be     cos / (1 + sin/cos)       The other will be similar.
But there is nothing to cancel out yet.
The two terms have to simplified [ Step 2]
Then combined [ Step 3]
At this point, you will be able to factor and cancel [ Step 4]
0
 
LVL 3

Author Comment

by:Computer Guy
ID: 40447620
Not sure how to simplify them.
0
 
LVL 27

Expert Comment

by:d-glitch
ID: 40447754
The problem with this term   cos / (1 + sin/cos)   is that there is a fraction in the denominator.
How do you simplify that?    

If the term were   3 / (1 + 2/7)  what would you do?
0
 
LVL 27

Expert Comment

by:d-glitch
ID: 40448005
I don't imagine that this identity is particularly useful, but it is quite simple.

The only trig you need to know is that   tan = sin/cos   and   cot = cos/sin
The rest is simple algebra.

The way to solve this is to assume that it is solvable and plug away.  It is really a 60 second problem.
0
 
LVL 3

Author Comment

by:Computer Guy
ID: 40448176
I know what tan and cot equal. I just don't know what to do with the (1+sin/cos)
0
 
LVL 27

Accepted Solution

by:
d-glitch earned 2000 total points
ID: 40448250
After substituting for   tan  

The first term becomes   cos / (1 + sin/cos)  

To simplify this you have to eliminate the fraction in the denominator (bottom).
You can multiply this term by   cos / cos   to get   cos² / (cos + sin)
You have to do something similar to the second term.
That will complete [ Step 2]
0

Featured Post

New feature and membership benefit!

New feature! Upgrade and increase expert visibility of your issues with Priority Questions.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

This article seeks to propel the full implementation of geothermal power plants in Mexico as a renewable energy source.
Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…
Suggested Courses

765 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question