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TrigReduce

TrigReduce[expr]
rewrites products and powers of trigonometric functions in expr in terms of trigonometric functions with combined arguments.
  • TrigReduce operates on both circular and hyperbolic functions.
  • 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.
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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:
ChebyshevU[n, Cos[x]] is related to Sin:
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:
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