SOLUTION: Having trouble proving the following half angle identity: csc^2 x/2 = 2 sec X/ sec -1. If you could please explain the steps. I started working on the left side, used the sin a/2

Algebra ->  Trigonometry-basics -> SOLUTION: Having trouble proving the following half angle identity: csc^2 x/2 = 2 sec X/ sec -1. If you could please explain the steps. I started working on the left side, used the sin a/2       Log On


   

Question 965160: Having trouble proving the following half angle identity: csc^2 x/2 = 2 sec X/ sec -1. If you could please explain the steps. I started working on the left side, used the sin a/2 identity formula and flipped it for CSC.
Csc^2x/2 = 2/1-cos X. This is where I got stuck. Not sure if I'm on the right track.
Thank you in advance for your help!
Found 2 solutions by t0hierry, lwsshak3:
Answer by t0hierry(194) About Me  (Show Source):
You can put this solution on YOUR website!
csc^2 x/2 = 1/sin^2(x/2) = 2/(1-cosx)
lol I'm stuck too.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Prove:
csc^2 x/2 = 2 sec X/ sec -1
start with right side:
2secx%2Fsecx-1
%282%2Fcosx%29%2F%281%2Fcosx-1%29
%282%2Fcosx%29%2F%28%281-cosx%29%2F%28cosx%29%29
2%2F%281-cosx%29=1%2Fsin%5E2%28x%2F2%29=csc%5E2%28x%2F2%29
verified: right side=left side
notes:
sin%28x%2F2%29=sqrt%28%281-cosx%29%2F2%29
sin%5E2%28x%2F2%29=%281-cosx%29%2F2
csc%5E2%28x%2F2%29=1%2Fsin%5E2%28x%2F2%29=2%2F%281-cosx%29