Question

prove:
cos*2x=csc*2x-2/csc*2x

Answer 1

I think you must be usint * as the power to, as in ^

right side: (csc^2 x - 2)/csc^2 x
(1-2sin^2x) = 1-2(1-cos^2x)=-1+2cos^2x
which is clearly not an identity.

So I am not certain what your problem is.

Answer 2

Your use of * in the last 3 posts will cause confusion

traditionally
* means multiplication
/ means division and
^ means "to the exponent"

so you want to say
cos^2 x=csc^2 x-2/csc^2 x

but that statement is not true for all x's, I just tried any x and it did not work.
Use brackets to establish the proper order of operations.