5.4.5

Double Angle Formula

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Double Angle Formulae

The double angle formulae are special cases of the angle addition formulae where A=BA = B.

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Sine

  • The double angle formula for sine is:
    • sin2AsinAcosA+cosAsinA2sinAcosA\sin2A \equiv \sin A\cos A + \cos A\sin A\equiv 2\sin A\cos A
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Cosine

  • The double angle formula for cosine is:
    • cos2AcosAcosAsinAsinAcos2Asin2A\cos2A \equiv \cos A\cos A - \sin A\sin A\equiv \cos^2A - \sin^2A
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Cosine cont.

  • We can find equivalent identities by using the fact that cos2A+sin2A=1\cos^2A + \sin^2A = 1:
    • cos2A12sin2A2cos2A1\cos2A\equiv 1-2\sin^2A\equiv 2\cos^2A-1
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Tangent

  • The double angle formula for tangent is:
    • tan2AtanA+tanA1tanAtanA2tanA1tan2A\tan2A\equiv \frac{\tan A+\tan A}{1 - \tan A \tan A}\equiv\frac{2\tan A}{1-\tan^2 A}

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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