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Here s a reminder of the angle sum formulas.
Double angle formula for sine math. Sin 2x 2 sin x cos x. Sin 2θ 2sinθcosθ. Sin a b sinacosb cosasinb. Sin 2 θ 2 sin θ cos θ sin 2 theta 2 sin theta cos theta sin 2θ 2sin θ cos θ cos 2 θ cos 2 θ sin 2 θ.
A b 2θ. Theta θ and the. Cos a b cosacosb sinasinb. If you let θ a b in the double angle identities then you get.
Sin 2 x 2 sin x cos x cos 2 x cos 2 x sin 2 x 2 cos 2 x 1 1 2 sin 2 x tan 2 x 2 tan x 1 tan 2 x begin aligned sin 2x 2 sin x cos x cos 2x cos 2 x sin 2 x 2 cos 2 x 1 1 2 sin 2 x tan 2x frac 2 tan x 1 tan 2 x end aligned sin 2 x cos 2 x tan 2 x 2 sin x cos x cos 2 x sin 2 x 2 cos 2 x 1 1 2 sin 2 x 1 tan 2 x 2 tan x. Sin 2θ sinθcosθ cosθsinθ. Then the following formulas are used for the double angle. 1 tan 2 x sec 2 x cos 2 x.
The double angle formula for sine comes from using the trig identity for the sine of a sum sin α β sinαcosβ cosαsinβ. We can use our formula for the sine of a double angle to find the required value. 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. 2 theta 2θ is the double angle.
Displaystyle frac 1 tan 2 x sec 2 x cos 2 x sec2x1 tan2x.
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