5.2 Verifying Identities

What is an identity?

Guidelines for Verifying Identities 1.Work with one side of the equation at a time. Use the more complicated side. 2.Try to: factor, add fractions, square a binomial, create a monomial denominator 3.Look to use the fundamental identities—note which functions are in the final expression you want. 4.If all else fails, convert everything to sines and cosines 5.Try something! Even attempts that lead to dead ends provides insight. **There is no well defined set of rules or procedure to follow. This is best learned by practice. **Remember, these are NOT equations—you cannot use operations such as adding/subtracting/multiplying/dividing/squaring both sides!

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

What’s More Complicated? 1.Fractions with a binomial (or longer) denominator 2.Fractions 3.Addition/Subtraction 4.Multiplication Some Hints To Try 1.See squared terms?  Think Pythagorean Identities 2.Don’t see any algebraic steps  Think converting to sines and cosines 3.See multiple fractions  Combine them 4.See one fraction with a monomial denominator  Make it two.

Practice

Practice