Trigonometric Identities

(cos x)/(sec x -1) - (cos x)/(sec x + 1) = 2 cos^3 x csc^2 x

Get a common denominator of  (secx + 1) (secx - 1)  on the left

[cosx (secx + 1) - cosx (secx -1)  ]   / [ (secx + 1) (secx -1)]

Simplify

[1 + cosx - 1 + cosx] / [sec^2 x - 1]     

Remember   [ tan2x + 1 = sec^x] ....  so....  [ sec^x - 1  = tan^2x]

[2cosx] / [tan^2x] =

[2cosx] / [ sin^2x / cos^2x]  =

[2cosx] [cos^2x / sin^2x ]  =

2cos^3x  * [ 1 / sin^2x]  =

2cos^3x * csc^2x

And the left = the right

Thank you very much! I have trouble with these...