By practicing and practicing, you will be more and more skillful in this subject.
This is the list of the simplest formulas for trigonometry identity.

Then there are some formulas, that is rather difficult than the previous ones. Here they are :

From these formulas, we can derive another harder formulas like some formulas below.

There are also some useful shorthand formulas derived form the formulas above. Think about the formula for

This fomula is derived from the base formula

Using this formula directly despite of writing of the process from the basic formula will reduce our work in solving the identity problems.
Below I want to present one tricky formula than can be directly used in some situations.

This is beautiful I think. Through many practicing to solve problems, you can develop your skill and expanding your scoop and overview about trigonometry identities. I have some solved exercises for you. You can see how they solved. You may try your best with your own way to solve the problem. What I have worked for you just one of the some ways that may be exist. Here is the link you can use to download the solved problems. Wish you luck.... (email me for the password).
