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Trigonometric Expressions

TrigExpand[expr]expand trigonometric expressions out into a sum of terms
TrigFactor[expr]factor trigonometric expressions into products of terms
TrigFactorList[expr]give terms and their exponents in a list
TrigReduce[expr]reduce trigonometric expressions using multiple angles

Functions for manipulating trigonometric expressions.

This expands out a trigonometric expression.
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This factors the expression.
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And this reduces the expression to a form linear in the trigonometric functions.
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TrigExpand works on hyperbolic as well as circular functions.
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TrigReduce reproduces the original form again.
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Mathematica automatically uses functions like Tan whenever it can.
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With TrigFactorList, however, you can see the parts of functions like Tan.
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TrigToExp[expr]write trigonometric functions in terms of exponentials
ExpToTrig[expr]write exponentials in terms of trigonometric functions

Converting to and from exponentials.

TrigToExp writes trigonometric functions in terms of exponentials.
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TrigToExp also works with hyperbolic functions.
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ExpToTrig does the reverse, getting rid of explicit complex numbers whenever possible.
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ExpToTrig deals with hyperbolic as well as circular functions.
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You can also use ExpToTrig on purely numerical expressions.
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