are all formulas. They are neatly gathered in the Dummies website under Trig for PreCalculus
http://www.dummies.com/how-to/content/trig-identities-for-precalculus.html
you have to show both sides of the equal sign are the same.
First let's review what is an identity (these are the Trigonometry Identities), I like the Dummies series of books because they explain things clearly and as simply as possibly.
Similar to the Illistration above: http://www.dummies.com/how-to/content/trig-identities-for-precalculus.html
Now that we have reviewed the Trig Identities for Pre-Cal, lets look at some videos: https://www.youtube.com/watch?v=A1iKe4HkoXc
Mr. McLogan explains that Verifying a Trig Identity you need to:
Pick the most complicated side of the = sign
Apply the operations: +, -, *, Factor or in-other-words - make it simpler if possible
Apply identities (this is where you reference the Dummies list to see if you can convert to something on this list)
Keep trying - sometimes the first application of an identity doesn't work, then try a different identities
If you let Mr McLogan's video continue to run - he goes into several examples. One of these may help you.
Khan Academy has 39 videos on Trig.
This review may help you to feel more comfortable with Trig Identities which will help you do the Verification faster. I don't think there are any shortcuts - except to feeling more comfortable with the Basic Trigonometric Identities that are outlines on the Dummies page.
https://www.youtube.com/watch?v=Jsiy4TxgIME&list=PLD6DA74C1DBF770E7