double angle identity

sin(2x) = 2sinxcosx (1)
cos(2x) = cos2x-sin2x=2cos2x-1=1-2sin2x (2)
tan(2x) = 2tanx1-tan2x (3)

These are all derived from their respective trigonometric addition formulas. For example,

sin(2x) = sin(x+x)
= sinxcosx+cosxsinx
= 2sinxcosx

The formula for cosine follows similarly, and the formula tangentPlanetmathPlanetmathPlanetmath is derived by taking the ratio of sine to cosine, as always.

The double angle identities can also be derived from the de Moivre identityMathworldPlanetmath.

Title double angle identity
Canonical name DoubleAngleIdentity
Date of creation 2013-03-22 12:14:31
Last modified on 2013-03-22 12:14:31
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 16
Author Wkbj79 (1863)
Entry type Theorem
Classification msc 26A09
Classification msc 33B10
Synonym double-angle identity
Synonym double angle formula
Synonym double-angle formula
Synonym double angle formulae
Synonym double-angle formulae
Related topic DeMoivreIdentity
Related topic AngleSumIdentity
Related topic AdditionFormulasForSineAndCosine