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

[Elijah the Wood]

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

 

[Sirus]

Please show us what you have tried so far.

 

[math_fortress]

Hmmm..that is tough...
I'm actually having trouble w/ questions similar to this too

 

[math_fortress]

on number 2...wouldn't you try to get both sides equal to "sin2x"?

 

[Elijah the Wood]

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)

 

[Elijah the Wood]

can anyone help?