I need a proof of this trignometric question

Question

(cosec x + cot x)^2=(sec x+1)/(sec x-1)

Answer 1

(cscx + cotx)² = (1/sinx + cosx/sinx)²

 

                      = [(1+cosx)/sinx]²

 

                      = (1+cosx)² / sin²x

 

                      = (1+cosx)² / (1 - cos²x)

 

                      = (1 + cosx)² / [(1 + cosx)(1 - cosx)]

 

                      = (1 + cosx)/(1 - cosx)

 

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