How do you prove a trig identity?
Category: Trigonometry »
Course: Pre-Calculus »
Identity ProofsThe process of proving trig identities doesn't have a lot of fans out there in the world. It's more like puzzle-solving than math, and doesn't accomplish anything real. After all, identity means "itself", so when you are asked to prove a trig identity, you are being asked to show something is itself, which inherently sounds pointless.Regardless, we've gotta get it done to get the grade! Here are some quick rules and tips to follow.Rules
- On each side of the equals sign, use basic facts, trig relationships, and algebra rules to change the initial expressions and show that they are indeed equal.
- Never perform an operation to both sides of the equation (such as multiplying both sides by $\sin(x)$). Only perform manipulations and changes.
- Turn functions into sine and cosine functions
- Obtain common denominators and combine terms if you have fractions
- Look for $\sin^2$ and $\cos^2$ terms
- Keep your goal in mind