posted by Urgh .
Establish the identity:
(1 - cos^2 0)(1 + cot^2 0) = 1
Let's use x instead of 0 as the angle, to avoid cnfusion with the number zero.
Remember that 1 - cos^2 x = sin^2 x
Also sin^2 x *cot^2 x = sin^2*cos^2/sin^2 = cos^2 x
With those steps, and sin^2 x + cos^2 x = 1, you should be able to prove this identity.