Simplify the following trigonometric expression csc(x)-cot(x)/sec(x)-1

Question

Simplify the following trigonometric expression as much as possible

Answer 1

Given trigonometrc expression Csc(x)-Cot(x)/Sec(x)-1

= [1/Sin(x)-Cos(x)/Sin(x)]/[1/cos(x)-1]

= [(1-Cosx)/Sinx]/[1-Cos(x)/Cos(x)]

= Cos(x)/Sin(x)

= Cot(x)