Sleuthing Out Identity Solutions
In This Chapter
Handling fractions with care
Maneuvering with handy algebraic tricks
Getting creative with math operations to prove identities
Proving a trig identity can be a simple chore, or it can be a challenge. The nice thing about an identity is that you know that it can be proved — it's an identity, for goodness sake. Some identities seem to just call out with the methods needed to prove them. “Look at me! Look at the three terms on the right that begging to be combined!” Other identities just sit there — daring you to do anything about them.
In this chapter, you find more techniques and suggestions for handling identities. You always want to find the simplest way, first . . . if there is a simplest way. If the easy road fails you, then get on this super highway of trigonometric maneuvers.
The ratio and reciprocal identities involve fractions. The half-angle identities use fractions. You just can't get away from them. Actually, an identity with fractions can work to your advantage. You can work toward getting rid of the fraction and, in the process, solve the problem. Some of the main techniques for working ...