Solve the Identity

cot (x)/ (csc(x)-1)= (csc(x)+1)/cot (x)

Left side

(cos/sin)/(1/sin -1)

cos /(1-sin)
multiply top and bot by (1+sin)
cos(1+sin)(1-sin^2)
or
(1+sin)/cos

right side
(1/sin +1) /( cos/sin)

(1+sin)/cos
same