Trig identity problem in prep for a quiz tomorrow?

Question

Hi everyone, I need help with a trig identify problem
http://img180.imageshack.us/img180/6640/70077949cj0.jpg
steps would be greatly appreciated =) thanks

Oh, and I'm trying to prove that it's equal

I can't plug in numbers because I have to solve it using cosines and sines, so far i have 1-cosx/1+cosx = csc^2-2cotxcscx + cot^2x

and chaging stuff around i get stuck at
1-cosx/1+cosx = (1-2cosx+cos^2)/(1-cos^2x)

Answer 1

we have
csc ^2(x) - 2cscx cotx + cot ^2(x)
= (cscx - cotx ) ^2
= [ ( 1 / sinx) - (cosx / sinx)] ^2
= [( 1 - cosx) / sinx ] ^2
= ( 1 - cosx) ^2 / sin^2( x)
from , sin ^2 (x) = 1 - cos ^2 (x)
so
= ( 1- cosx) ^2 / [ 1 - cos ^2(x)]
= ( 1 - cosx) ^2 / [ ( 1 - cosx) ( 1 + cosx)]
= ( 1 - cosx) / ( 1 + cosx)
then

[(1 - cosx) / ( 1 + cosx)] = csc ^2x - 2cscxcotx + cot ^2x

Answer 2

(1 - cosx) / (1 + cosx) =? (cscx - cot^2x)^2
(1 - cosx)(1 - cosx) / [(1 - cosx)(1 + cosx)] =? (cscx - cot^2x)^2

(1 - cosx)^2 / (1 - cos^2x) =? (cscx - cot^2x)^2
(1 - cosx)^2 / sin^2x =? (cscx - cot^2x)^2
[(1 - cosx) / sinx]^2 =? (cscx - cot^2x)^2
(cscx - cotx)^2 ≠ (cscx - cot^2x)^2

Edit:
(1 - cosx)^2 / (1 - cos^2x) ≡ (cscx - cotx)^2
Edit #2:
...meant to say
(1 - cosx) / (1 + cosx) ≡ (cscx - cotx)^2

Answer 3

1 - cos(30º) / 1+ cos(30º) = (1/sin(30º) - 1/tan²(30º) )²
1 - 0.8662 / 1 + 0.8662 = ((1 / (0.5) - 1 / (1.333))²
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now get ur calculator out