I'm a little confused how to start this problem:
1 + cosx + sinx
sinx 1 + cosx
Looks like a tricky one, these proofs can be unforgiving at times but if you get one to fall out it feels great.
Have a look at this list of identities
Table of Trigonometric Identities
Then remember that
Try try to put everything one the left hand side in terms of sin(x)