"Strategies for Proving Identities"
Strategies for Proving Identities 1. Learn the basic identities so they come to mind readily. 2. Pick the side you wish to work with. Usually it is easier to start with the more complicated side. 3. Look for algebraic things to do: a. If there are two terms, you want only 1 i. add fractions ii. factor something out b. Multiply by a clever form of 1 i. to multiply a numerator or denominator by its conjugate or ii. to get a desired expression in the numerator or denominator. c. Do any obvious algebra such as distribute like terms, squaring, or multiplying polynomials. 4. Look for trigonometric things to do. a. Look for familiar trig expressions like: sin 1 cos2 cos sec cos b. If there are squares of functions, think of Pythagorean properties. c. Reduce the number of different functions, transforming them to the ones you want in the answer. 5. Keep looking at the answer to make sure you are headed in the right direction. 6. When you don’t know what to do, just try something!! You are allowed to simplify both sides of the = sign, however nothing can be moved across the = sign and nothing can be added, subtracted, multiplied, or divided to the entire identity. Examples: 1. csc sin 1 2. cot 2 sec2 tan2 csc2 cos sin 3. sec2 tan 2 sec csc 4. (tan2 x 1)(cos2 x 1) tan2 x 5. tan x cot x sec x csc x