Prove tan(x)-sin(x)/2tan(x) = sin^2(x/2)

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Homework Help Overview

The discussion revolves around proving a trigonometric identity involving tangent and sine functions, specifically the equation tan(x) - sin(x)/2tan(x) = sin^2(x/2). Additionally, a second problem involving sin(2x) and its relationship with tangent and cotangent is presented.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss their attempts to manipulate the first identity and express uncertainty about their progress. There is a suggestion to equate both sides of the second identity to sin(2x). Some participants express difficulty with similar problems.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and seeking clarification. Some have provided partial progress on the identities, while others are questioning the direction of their reasoning. There is no clear consensus yet on the approaches being taken.

Contextual Notes

Participants express a need for assistance and indicate that they are grappling with the identities presented, suggesting a potential lack of foundational understanding or confidence in their methods.

Elijah the Wood
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I'm retarded...any help would be much congratulated...and i have two problems that are bugging me fiercing

Prove the given identity:

1)
tan(x)-sin(x)/2tan(x) = sin^2(x/2)



2)
sin2x = 1 / tanx + cot2x
 
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Please show us what you have tried so far.
 
Hmmm..that is tough...
I'm actually having trouble w/ questions similar to this too
 
on number 2...wouldn't you try to get both sides equal to "sin2x"?
 
1)
tan(x)-sin(x)/2tan(x) = sin^2(x/2)
1-sin(x)/2 = sin^2(x/2)

(That's as far as I've gotten on this one...but i don't know if I'm in the right direction or what to do next?)

2)
sin2x = 1 / tanx + cot2x
2sin(x)cos(x) = ''
sin(x) * cos(x) * sin(x) = ''

(The same from #1 applies to this problem)
 
can anyone help?
 

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