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double angle identity∗
Wkbj79†
2013-03-21 13:19:06
The double angle identities are
sin(2x)
cos(2x)
tan(2x)
=
2 sin x cos x
(1)
2
2
2
2
cos x − sin x = 2 cos x − 1 = 1 − 2 sin x
2 tan x
=
1 − tan2 x
=
(2)
(3)
These are all derived from their respective trigonometric addition formulas.
For example,
sin(2x)
=
sin(x + x)
=
sin x cos x + cos x sin x
=
2 sin x cos x
The formula for cosine follows similarly, and the formula tangent is derived
by taking the ratio of sine to cosine, as always.
The double angle identities can also be derived from the de Moivre identity.
∗ hDoubleAngleIdentityi
created: h2013-03-21i by: hWkbj79i version: h31623i Privacy
setting: h1i hTheoremi h26A09i h33B10i
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