You made a mistake for (1-cosx)(1-cosx). It should give -2cosx which cancels out with the other 2cosx, so you only have 2 + 2cos2x on top. Convert the 2cos2x to 2(1-sin2x) and you should easily get the answer.

hello thank you for your help but unfortunately I'm stuck again
please click the link and help me identify the mistake if you can : https://imgur.com/a/yWJZfbB

There's no mistake, you almost have the answer. a=4 and b=-2 .

but it's not in the form acosec²x+ b though?

1/sin2x = cosec2x. sin2x cancels out for the 2nd term.

oh ok get it now, thx