The tips and tricks that I have found helpful are separating and combining fractions. This is helpful because it allows us to reduce a trig function in order to simplify or verify it. Furthermore, altering fractions allows us to substitute trig functions with identities.
When verifying trig functions, you can use identities and substitute one trig function for another. Furthermore. You can combine like terms and simplify. Another way to verify trig functions is to multiply by the conjugate.