|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|
TrigExpand works on hyperbolic as well as circular functions.
TrigReduce reproduces the original form again.
The Wolfram System automatically uses functions like Tan whenever it can.
|TrigToExp[expr]||write trigonometric functions in terms of exponentials|
|ExpToTrig[expr]||write exponentials in terms of trigonometric functions|
TrigToExp writes trigonometric functions in terms of exponentials.
TrigToExp also works with hyperbolic functions.
ExpToTrig does the reverse, getting rid of explicit complex numbers whenever possible.
ExpToTrig deals with hyperbolic as well as circular functions.
You can also use ExpToTrig on purely numerical expressions.