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Double Angle

This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.

Double Angle

$\sin (2 a) = 2 \sin a \cos a$

$\begin{aligned} \cos (2 a) & = \cos^{2} a - \sin^{2} a \\ = 2 \cos^{2} a - 1 \\ = 1 - 2 \sin^{2} a \end{aligned}$

$\tan (2 a) = \frac{2 \tan a}{1 - \tan^{2} a}$

Related Glossary Terms

Angle addition, Half angle, Sinusoidal function, Trigonometric identities, Trigonometric substitution

Index

Chapter 1 - An Overview of Trigonometry

Chapter 4 - The Chain Rule

Chapter 9 - Trigonometric Substitution

Glossary and deeper reading · 1 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

Double angle identity
A double angle identity rewrites a trigonometric expression with twice an angle. For example, cos(2θ)=2cos²θ−1 and sin(2θ)=2sin θ cos θ. The cosine identity gives cos²θ=[1+cos(2θ)]/2, which can simplify a trigonometric integral. These identities follow from the angle addition formulas.

Double angle identity

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