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Double-Angle Formulas

Formulas expressing trigonometric functions of an angle 2x in terms of functions of an angle x,

sin(2x)=2sinxcosx
(1)
cos(2x)=cos^2x-sin^2x
(2)
=2cos^2x-1
(3)
=1-2sin^2x
(4)
tan(2x)=(2tanx)/(1-tan^2x).
(5)

The corresponding hyperbolic function double-angle formulas are

sinh(2x)=2sinhxcoshx
(6)
cosh(2x)=2cosh^2x-1
(7)
tanh(2x)=(2tanhx)/(1+tanh^2x).
(8)

See also

Half-Angle Formulas, Hyperbolic Functions, Multiple-Angle Formulas, Prosthaphaeresis Formulas, Trigonometric Addition Formulas, Trigonometric Functions, Trigonometry Explore this topic in the MathWorld classroom

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Cite this as:

Weisstein, Eric W. "Double-Angle Formulas." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Double-AngleFormulas.html

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