Prove Trig Identities: sec(2x) - tan(2x) & cos(2x)/(1 + sin(2x))

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Homework Help Overview

The discussion revolves around proving two trigonometric identities involving secant, tangent, and cosine functions. The identities are presented with slight variations in their starting positions, prompting participants to explore their relationships and transformations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss their attempts to manipulate the identities, with one participant expressing difficulty after reaching a certain expression. Questions arise about the implications of the cosine function and how it relates to the identities being proven.

Discussion Status

The discussion is ongoing, with participants sharing their progress and questioning the next steps. Some guidance is offered regarding the relationship between the expressions, but no consensus or resolution has been reached yet.

Contextual Notes

Participants are working under the constraints of homework rules, and the identities presented have variations that may influence their approaches. There is an emphasis on understanding the relationships between the trigonometric functions involved.

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Homework Statement


Teacher gave this identity twice to us but the starting position slightly varies.

Prove sec(2x) - tan(2x) = (cos(x)-sin(x))/(cos(x) + sin(x))

Prove cos(2x)/(1 + sin(2x)) = tan(pi/4-x)


Homework Equations


pretty much all trig identities


The Attempt at a Solution



I get to (1-sin(2x))/cos(2x) = (cos(x)-sin(x))/(cos(x) + sin(x)) and then I'm stumped.
 
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Welcome to PF!

Hi Hockeystar! Welcome to PF! :wink:
Hockeystar said:
I get to (1-sin(2x))/cos(2x) = (cos(x)-sin(x))/(cos(x) + sin(x))

ok so far :rolleyes:

now what is cos(2x) ? :smile:
 
cosx - sinx(cosx + sinx). How does that help me cancel out something?
 
Hockeystar said:
cosx - sinx(cosx + sinx). How does that help me cancel out something?

You mean (cosx - sinx)(cosx + sinx) …

It doesn't have to cancel to help :wink:

think! look at the RHS!
 

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