Thursday, October 20, 2011

Strategies for Proving Trigonometric Identities

From all the trig identity problems that I have solved, I have come up with these strategies:
  1. Convert everything to sine and cosine. In other words, get rid of the tangents, cotangents, cosecants and secants.
  2. Work with the more complex side first: it's often easier to simplify expressions that are complex than to make the more simple side equal to the more complicated one.
  3. Use common denominators: if the two sides have different denominators, how can they equal to each other?
  4. If the sines and cosines have 2 or 4 as their exponents, then try to use the identity sin2 θ + cos2 θ = 1 to simplify.
  5. Don't just work on one side: unless one of the sides is a simple value like "1" or "sin θ", it's usually a good idea to try to make the two sides meet in the middle.
  6. Factor: A lot of times it is important to factor, as this would often help simplifying the sides