# TrigFactor

TrigFactor[expr]

factors trigonometric functions in expr.

# Details • TrigFactor operates on both circular and hyperbolic functions.
• TrigFactor splits up sums and integer multiples that appear in arguments of trigonometric functions, and then factors resulting polynomials in trigonometric functions, using trigonometric identities when possible.
• TrigFactor automatically threads over lists, as well as equations, inequalities, and logic functions.

# Examples

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## Basic Examples(3)

Factor a trigonometric expression into a product of terms:

Factor a hyperbolic trigonometric expression:

Factor trigonometric expressions of several variables:

## Scope(6)

Factor a univariate trigonometric expression:

Factor a multivariate trigonometric expression:

Factor a hyperbolic trigonometric expression:

Factor a rational combination of trigonometric functions:

TrigFactor threads over equations and inequalities:

## Applications(2)

Solve a trigonometric polynomial equation:

Reduce it to elementary trigonometric equations:

Detect common roots of trigonometric polynomials:

Common roots of and are the roots of :

Using the original polynomials yields a more complicated result:

To show that the root sets are equal, it suffices to check within one period:

## Properties & Relations(2)

Compare TrigExpand, TrigReduce, and TrigFactor on the same expression:

TrigFactor threads elementwise over lists, inequalities, equations, and logical operations:

## Possible Issues(1)

A trigonometric expression can be factored in many different ways: