CSC - COS X COT = SIN

writing your equation the way you did is indeed a mathematical SIN

Did you mean ...
cscx - cosxcotx = sinx ?
and are we proving the identity?

If so, then
LS = 1/sinx - cosxcosx/sinx
= (1 - cos^2 x)/sinx
= sin^2 x / sinx
= sinx
= RS