Question

\[\sqrt{1-\cos \alpha/1+\cos \alpha}=\csc \alpha-\cot \alpha\]

Answer 1

identities

Answer 2

Square both sides and try.

Answer 3

with this kind of problem you're supposed to work on 1 side only

Answer 4

With this sort of problem you're not going to get anywhere with the square root there, so try and get rid of it first and see what you get.

Answer 5

Doesn't actually seem to be an identity? See: http://www.wolframalpha.com/input/?i=Plot [{Csc[x]-Cot[x]%2C+%28%281-Cos[x]%29%2F%281%2BCos[x]%29%29^.5}%2C+{x%2C0%2C10*Pi}]

Squaring both sides would make it look like one when it is not.

Answer 6

For example try \[\alpha=3\pi/2\]
Csc[3*Pi/2] - Cot[3*Pi/2] = -1
Sqrt[(1 - Cos[3*Pi/2])/(1 + Cos[3*Pi/2])] = 1