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

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The discussion focuses on proving two trigonometric identities. The first identity, tan(x) - sin(x)/(2tan(x)) = sin^2(x/2), is being approached by simplifying both sides, with one participant expressing uncertainty about their progress. The second identity, sin(2x) = 1/tan(x) + cot(2x), is also under scrutiny, with suggestions to manipulate both sides to achieve a common form. Participants are seeking guidance on how to proceed with these proofs, indicating a need for clarity in trigonometric transformations. Overall, the thread highlights challenges in understanding and proving specific trigonometric identities.
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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