Verifying trigonemetric identities is quite a complicated process.
To start with, u need to combine like terms and trigonometric functions together. Then you need to put all trigonometric terms on one side of the equation. After this you need to apply a trigonometric identity if there is the need for one. Then you would factor if it needs to be factored. Isolate the trigonometric function to one side, and finally solve for the variable. Within this we use algebra, trig functions, and a lot of simplifying.