TrigFactorList
TrigFactorList[expr]
factors trigonometric functions in expr, yielding a list of lists containing trigonometric monomials and exponents.
Examples
open all close allBasic Examples (2)
Scope (4)
Compute the factors of a univariate trigonometric expression:
TrigFactorList[Sin[x] ^ 2 - Cos[x] ^ 2]Compute the factors of a univariate hyperbolic trigonometric expression:
TrigFactorList[Sinh[x] ^ 2 + Tanh[x] ^ 2]Compute the factors of a multivariate trigonometric expression:
TrigFactorList[Sin[x - 3y] ^ 2 - Cos[x] ^ 2]Compute the factors of a rational combination of trigonometric functions:
TrigFactorList[Cosh[x + y] / (Sin[x] ^ 2 - Cos[x] ^ 2) + 1 / Sinh[x]]Applications (2)
Show that a trigonometric expression is a perfect square:
e = 4Cosh[x] ^ 4 - 4Cosh[x] ^ 2;Compute the factors and note that the constant factor is positive:
fac = TrigFactorList[e]Extract the exponents of nonconstant factors:
exp = Transpose[Rest[fac]][[2]]Check that every factor has an even exponent and thus 
is a square:
AllTrue[exp, EvenQ]Compute a common divisor of two trigonometric expressions:
f1 = TrigFactorList[Cos[x] ^ 2Sin[x] ^ 2 + Sin[x] ^ 2]f2 = TrigFactorList[4 Cos[x] ^ 4 - Cos[x] ^ 2Sin[2 x] ^ 2 + Sin[2 x] ^ 4 / 16]ReplaceList[{f1, f2}, {{___, {a_, b_}, ___}, {___, {a_, c_}, ___}} :> {a, Min[b, c]}]Text
Wolfram Research (1996), TrigFactorList, Wolfram Language function, https://reference.wolfram.com/language/ref/TrigFactorList.html.
CMS
Wolfram Language. 1996. "TrigFactorList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TrigFactorList.html.
APA
Wolfram Language. (1996). TrigFactorList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TrigFactorList.html