Can you prove the following two difficult trigonometric identities?

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Discussion Overview

The discussion revolves around proving two trigonometric identities involving secant, tangent, sine, and cotangent functions. The identities are presented in a mathematical context, with participants exploring the possibility of providing proofs or methods for verification.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant presents two trigonometric identities for proof, expressing uncertainty about their validity.
  • Another participant offers assistance by highlighting the availability of a LaTeX compiler for formatting mathematical expressions, suggesting that it could aid in the discussion.
  • A third participant expresses gratitude for the information about the LaTeX compiler, indicating a willingness to engage further.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the proofs of the identities, and multiple viewpoints regarding the use of LaTeX and the identities themselves remain present.

Contextual Notes

Participants have not yet provided detailed proofs or explored the identities in depth, and there may be assumptions regarding the participants' familiarity with LaTeX and trigonometric identities.

DrLiangMath
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Can you prove the following?

[sec(x)]^6 - [tan(x)]^6 = 1 + 3*[tan(x)]^2*[sec(x)]^2

[sin(x)]^2*tan(x) + [cos(x)]^2*cot(x) + 2*sin(x)*cos(x) = tan(x) + cot(x)

If not, the following free math tutoring video shows you the method:

 
Mathematics news on Phys.org
@Dr. Liang: We have a LaTeX compiler here that you can use to type out the equations. If you don't know LaTeX reply to this to see how the coding works. The basics are simple and we have a Forum to show you how to do more complicated work.
[math]sec^6(x) - tan^6(x) = 1 + 3 ~tan^2(x) ~ sec^2(x)[/math]

[math]sin^2(x) ~ tan(x) + cos^2(x) ~ cot(x) + 2 ~ sin(x) ~ cos(x) = tan(x) + cot(x)[/math]

-Dan
 
Hello Dan,

Thank you so much for your kindness and help! I didn't notice a LaTeX compiler is available in the forum.

Derek
 
This is useful information
 

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