A LevelMaths: Pure 3CIERevision Notes3. Trigonometry3.2 Compound & Double Angle Formulae3.2.2 Double Angle Formulae

Double Angle Formulae (CIE A Level Maths: Pure 3)

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Roger

Last updated

19 May 2023

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Double Angle Formulae

What are the double angle formulae?

The double angle formulae are derived from the 'A+B' versions of the compound angle formulae:
- $\sin (2 A) \equiv 2 \sin A \cos A$
- $\cos (2 A) \equiv \cos^{2} A - \sin^{2} A$
  - $\cos (2 A) \equiv 2 \cos^{2} A - 1$
  - $\cos (2 A) \equiv 1 - 2 \sin^{2} A$
- $\tan (2 A) \equiv \frac{2 \tan A}{1 - \tan^{2} A}$

Double Angle Forms Illustr 1_sin, A Level & AS Maths: Pure revision notes Double Angle Forms Illustr 2_cos, A Level & AS Maths: Pure revision notes Double Angle Forms Illustr 3_tan, A Level & AS Maths: Pure revision notes

Examiner Tip

The double angle formulae can be found in the formulae booklet – make sure you know where to find them.
Look out for problems containing sinAcosA or an equation that contains both a double angle and a single angle.

Worked example

Double Angle Forms Example, A Level & AS Maths: Pure revision notes

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Previous:3.2.1 Compound Angle FormulaeNext:3.2.3 R addition formulae Rcos Rsin etc

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.