Proving trig identities is a bit like solving a puzzle: if it doesn’t work this way, try that way . . . !
As was said of the Grinch: “he puzzled and puzzled ‘till his puzzler was sore.” (Dr. Seuss)
When you are studying trigonometry in your math course (grade 11 or 12 ?) you likely have to practice proving trigonometric identities. And you don’t want to keep on puzzling and puzzling ‘till your puzzler is sore, so some strategies to aid you in your puzzling might not go amiss.
There is no one RIGHT way to prove a trig identity. There are usually many ways to get from start to finish. And there are many tips and tricks to help you along the way. Try this Tips and Tricks sheet, and see if it helps at all. Happy Puzzling!