# Trig Identities

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### When to Factor a Trigonometry Identity

You’ll know that you need to factor a trig identity when powers of a particular function or repeats of that same function are in all the terms on one side of the identity.

### Break Up or Combine Fractions to Solve a Trigonometry Identity

A trig identity with fractions can work to your advantage; you’re given a plan of attack. You can work toward getting rid of the fraction and, in the process, solve the problem. Two of the main techniques

### How to Remove a Third Angle to Solve a Trigonometry Identity

Sum and difference identities usually involve two different angles and then a third combined angle. When proving these trig identities, you often need to get rid of that third angle. The following example

### Find Opposite-Angle Trigonometry Identities

The opposite-angle identities change trigonometry functions of negative angles to functions of positive angles. Negative angles are great for describing a situation, but they aren’t really handy when it

### Reciprocal Identities

A big advantage of trig expressions and equations is that you can adjust them in so many ways to suit your needs. The basic reciprocal identities here are the ones people use most frequently.

### Sum-to-Product Identities

The sum to product identities are useful for modeling what happens with sound frequencies. Think of two different tones represented by sine curves. Add them together, and they beat against each other with

### Product-to-Sum Identities

The trig product-to-sum identities look very much alike. You have to pay close attention to the subtle differences so that you can apply them correctly. Even though the product looks nice and compact,

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