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Built-in Mathematica Symbol

TrigReduce

TrigReduce[expr]
rewrites products and powers of trigonometric functions in expr in terms of trigonometric functions with combined arguments.

Given a trigonometric polynomial, TrigReduce typically yields a linear expression involving trigonometric functions with more complicated arguments.

TrigReduce automatically threads over lists, as well as equations, inequalities and logic functions.

TrigReduce operates on hyperbolic trigonometric functions:

Manipulation with polynomials is performed using modular arithmetic:

Compare with the reduction over rationals:

Find the period of a trigonometric polynomial:

Verification:

ChebyshevT[n, Cos[x]] reduces to Cos[n x]:

ChebyshevU[n, Cos[x]] is related to Sin[n x]:

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

TrigReduce threads over lists, inequalities, equations and logical operations:

The value of the option Modulus must be an integer:

TrigReduce requires explicit trigonometric functions:

Use ExpToTrig to convert exponential to trigonometric functions:

Reducing constants might not always give the desired effect: