Question

sin x - cos x / sec x - csc x = cos x / csc x

Answer 1

Change everything to sin and cos 1st.

Answer 2

are you able to demonstrate @ehuman

Answer 3

For instance:
sinx - cosx/ secx-cscx

= sinx - cosx
-------------
1 1
-------------
cosx sinx

Answer 4

cosx/cscx

= cosx 1
-----------
1 sinx

Answer 5

Do that first, then look for transformations to get everything to either sin or cos.

Answer 6

im unsure on how

Answer 7

@ehuman