How to verify (sin-tan)(cos-cot)=(cos-1)(sin-1)

(sin-tan)(cos-cot)=(cos-1)(sin-1)
LS=( sin x - tan x)( cos x - cot x)
= {sin x(1 - 1/cos x)}{cos x(1 - 1/sin x)}
= [{sin x(cos x -1)}{cos x(sin x -1)}]/ (sin x* cos x)
= [{(cos x -1)}{(sin x -1)}]
= RS

Show:
(sin(x)-tan(x))(cos(x)-cot(x)) = (cos(x)-1)(sin(x)-1)

(sin(x)-tan(x))(cos(x)-cot(x)) =
= sin(x)cos(x) - sin(x)cot(x) - tan(x)cos(x) + tan(x)cot(x)
= sin(x)cos(x) - cos(x) - sin(x) + 1
= sin(x) (cos(x) -1) - cos(x) +1
= sin(x) (cos(x) -1) - (cos(x) -1)
= (cos(x) -1)(sin(x)-1)

If you have questions about any of the above steps, just let me know, but it is best for you to fill them in.