Theory of Intelligence
11TH•Mathematics•Trigonometric Identities•10.4 Double, Half and Triple Angles

10.4 Double-Angle Identities

Double-angle, half-angle, and triple-angle identities with worked examples.

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10.4 Double-Angle Identities

From the addition formulas with β=α\beta = \alpha:

sin⁡2α=2sin⁡αcos⁡α\sin 2\alpha = 2\sin\alpha\cos\alpha cos⁡2α=cos⁡2α−sin⁡2α=2cos⁡2α−1=1−2sin⁡2α\cos 2\alpha = \cos^2\alpha - \sin^2\alpha = 2\cos^2\alpha - 1 = 1 - 2\sin^2\alpha tan⁡2α=2tan⁡α1−tan⁡2α\tan 2\alpha = \dfrac{2\tan\alpha}{1 - \tan^2\alpha}

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