TrigExpand

TrigExpand[expr]

expands out trigonometric functions in expr.

Details

  • TrigExpand operates on both circular and hyperbolic functions.
  • TrigExpand splits up sums and integer multiples that appear in arguments of trigonometric functions, and then expands out products of trigonometric functions into sums of powers, using trigonometric identities when possible.
  • TrigExpand automatically threads over lists, as well as equations, inequalities, and logic functions.

Examples

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Basic Examples  (1)

Scope  (1)

TrigExpand operates on hyperbolic trigonometric functions:

Applications  (1)

Find ArcSin addition law:

Because of the multivaluedness of ArcSin this law does not hold everywhere:

Properties & Relations  (3)

TrigExpand and TrigReduce are, generically, inverses of each other:

The expressions are identical modulo trigonometric Pythagorean identities:

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

Use TrigExpand to construct a ChebyshevT polynomial:

Possible Issues  (1)

Expand trigonometric functions using half-angles:

Introduced in 1996
 (3.0)
 |
Updated in 2007
 (6.0)