How Do You Prove Trigonometric Identities with Minimal Equations?

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Homework Help Overview

The discussion revolves around proving a trigonometric identity involving tangent functions. Participants are attempting to manipulate both sides of the identity to show equivalence, focusing on the expression tan(x) - 1.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing how to approach the proof by manipulating the left and right sides of the identity. There are questions about dividing terms and applying trigonometric identities. Some participants express confusion about the steps involved, particularly regarding the use of formulas and the implications of their manipulations.

Discussion Status

The conversation is ongoing, with various participants providing insights and corrections. Some guidance has been offered regarding the manipulation of expressions, but there is still uncertainty about the correct approach to take. Multiple interpretations of the steps are being explored, and participants are questioning their assumptions and calculations.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can reference. There is a noted confusion about the application of certain trigonometric identities and the validity of specific algebraic manipulations.

  • #31
Student100 said:
That's fine. You just need to be careful, the = is saying something very precise.

what do you mean?
 
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  • #32
Evangeline101 said:
what do you mean?

The above line that I posted, you're saying the original expression is equal to 2tan(x), which isn't true. I know it was a typo, just make sure you're careful is all. No sense losing points on a typo. =)

The fixed solution looks fine to me.
 
  • #33
Student100 said:
The above line that I posted, you're saying the original expression is equal to 2tan(x), which isn't true. I know it was a typo, just make sure you're careful is all.

Okay, thanks for the help! :)
 
  • #34
Sorry for responding to this thread after it has been marked solved.

Ok, I am proving the exact same identity, I looked through the thread and the explanations were very helpful.

I wrote out the answer, and would just like to know if I have written the answer properly:

LS= tan x - 1
upload_2016-8-16_23-29-36.png
 
Last edited:
  • #35
Yes I think that's right now.
Hope you see it as simple now, and what you were missing.

One of the handful of formulae constantly useful to remember fluently, difference of two squares - and then difference of two n-th powers.
 

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