I feel terrible for making yet another thread, but I've been stuck on this for 30 mins:
LS=cos(2x)/(1-sin2x)
RS=(cosx+sinx)/(cosx-sinx)
Just use the identities I gave you otherwise.
Here, the trick is to spot that the numerator is a difference of two squares and that the numerator can be a square by using the Pythagorean identity,
This said, you get:
You then factor the denominator;
Some things cancel out, leaving the RS.
You can also see that it's the reverse process that Soroban posted