How would I prove the following trig question?

Question

[(1+cos x)/(1-cos x)] -[(1-cos x)/(1+cos x)]

Answer 1

  

The identity is  [(1+cos x)/(1-cos x)] - [(1-cos x)/(1+cos x)]

= ( 1 + cos x)( 1 + cos x) - (1 - cos x)(1 - cos x ) / (1 +cos x) ( 1 - cos x)

=(1 + cos x)²  - (1 - cos x)² / ( 1 - cos ² x)

= (1 + cos ² x + 2cos x ) - (1 + cos² x - 2 cos x ) / (sin ² x)       [ since sin ² x + cos ² x = 1]

= (1+ cos ²x +2cos x - 1 - cos² x + 2cos x ) / (sin² x)

= (4cos x ) /  sin² x .

= 4 cot x cosec x .