A little push on this trig identity

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Homework Help Overview

The discussion revolves around proving a trigonometric identity involving the tangent function and its relationship with cosine, specifically the identity \(\tan^2(x)= \frac {1-\cos(2x)} {1+\cos(2x)}\). Participants are exploring the use of double angle identities and their implications in the proof process.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster seeks clarification on the identity and its components, particularly questioning the derivation of \(\cos(2x)\) in terms of sine and cosine. Other participants discuss whether to prove the tangent identity or the cosine identity, with some suggesting that working with the right side may be more straightforward.

Discussion Status

Participants are actively engaging with the problem, with one suggesting a method to simplify the right side using double angle identities. There is acknowledgment of varying levels of comfort with the concepts involved, and guidance is being offered without reaching a consensus on the best approach.

Contextual Notes

There is an indication that some participants may be struggling with double angle identities, which could affect their approach to the problem. The original poster's request for clarification suggests a need for deeper understanding of the underlying concepts.

aisha
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A little push on this trig identity please

[tex]\tan^2(x)= \frac {1-\cos(2x)} {1+cos(2x)}[/tex]

I need a little push I know from my other post that [tex]\cos(2x)=\cos^2 (x) - \sin^2 (x)[/tex] (can someone explain why?)
 
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what is your questioin? proving the tan identity or the cos one?
 
I have to make the left hand side equal the right hand side I don't think it matters if you use cos or tan which ever one is easier.
 
It would be easier to work with the right side.
So it would be like:

[tex]\frac {1-\cos(2x)} {1+cos(2x)}[/tex]

[tex]\frac {1 - (1 - 2\sin^2x)}{1 + 2\cos^2x - 1}[/tex] Double angle identities

[tex]\frac{2\sin^2x}{2\cos^2x}[/tex] 2's cancel out

[tex]\tan^2x[/tex]
 
Thanks sooo much BLUE SODA I am not good with the double angle identity thanks again :smile:
 

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