Proving Trigonometric Identites

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Homework Help Overview

The problem involves proving a trigonometric identity that relates tangent, secant, and cosecant functions. The original poster presents an equation and seeks assistance in simplifying or transforming it to demonstrate the identity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various methods for simplifying the left-hand side (LHS) and right-hand side (RHS) of the equation, including converting functions into sine and cosine. There is uncertainty about how to manipulate the expressions correctly and whether to use common denominators.

Discussion Status

The discussion is active, with participants providing suggestions on how to approach the problem. Some guidance has been offered regarding the use of sine and cosine, and there are multiple lines of reasoning being explored without a clear consensus on the best method.

Contextual Notes

There is some ambiguity in the original expression, prompting participants to clarify the notation used. Additionally, the original poster expresses uncertainty about their approach and whether they are on the right track.

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Homework Statement



tan x + 1/tan x - 1 = sec x + csc x/sec x - csc x


Homework Equations





The Attempt at a Solution



Ive tried working with the right side and have gotten as far as sin x/cosxsinx - cos x/cosxsinx

Im not sure if I am just out to lunch, or on the right track. Any help would be awesome!

Thanks!
 
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Your expression is ambiguous the way you have written it. (Use either brackets or LaTeX)

Do you mean [tex]\frac{\tan(x)+1}{\tan(x)-1}=\frac{\sec(x)+\csc(x)}{\sec(x)-\csc(x)}[/tex] ?

If so, try working with the LHS: Express everything in terms of sines and cosines and then divide both the numerator and denominator by [itex]\sin(x)[/itex]
 
im not getting it. should i turn the 1 into sines or cosines? Or even how do I know to do that?
 
No you should turn the tan into sin/cos and the find common denominators, cancel, etc. etc.
 
Oh I did that too.

I had sin/cos + cos/cos all divided by sin/cos - cos/cos
 
Well a/c + b/c = (a+b)/c and also (a/b)/(c/d) = (ad)/(bc) I heard maybe you should use that.
 
Well I heard that gives me sin x cos x + cos^2 x / sin x cos x - cos ^2 x
 
Umm why haven't you canceled the cos
 
Your right, now I have sin x + cos x / sin x - cos x ?
 
  • #10
Now compare that to what you are trying to get to...
 
  • #11
I got it. I went with the RHS side though, and converted it to the LHS. Thanks for your help!
 

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