A LevelMaths: PureAQARevision Notes5. Trigonometry5.6 Compound & Double Angle Formulae5.6.2 Double Angle Formulae

Double Angle Formulae (AQA A Level Maths: Pure)

Revision Note

Author

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 are not included in the formulae booklet – you have to know them.
If you forget them, you can always derive them from the compound angle formulae (which are in the formula booklet) as shown above.

Worked example

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

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Previous:5.6.1 Compound Angle FormulaeNext:5.6.3 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.