LaTeX
\cos(2\theta)=\cos^2\theta-\sin^2\thetaVariables
- θ: angle
How to use this formula
Rewrites the cosine of a doubled angle using squared sine and cosine.
Important notes
- Equivalent forms are 2cos²θ−1 and 1−2sin²θ.
- Choose the form that matches the available information.
Quick example
For θ=45°, cos90°=1/2−1/2=0.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Equivalent forms are 2cos²θ−1 and 1−2sin²θ.
- The angle unit and the domain or branch of any inverse trigonometric function must be explicit.
- Use a consistent angle unit and verify the quadrant, periodicity, and domain restrictions of inverse functions.
Worked example
For θ=45°, cos90°=1/2−1/2=0.
Common mistakes
- Do not mix degrees and radians in Cosine Double-Angle Identity; use one angle convention throughout the calculation.
- Verify the result of Cosine Double-Angle Identity with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Cosine Double-Angle Identity in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\cos(2\theta)=\cos^2\theta-\sin^2\theta. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Cosine Double-Angle Identity used for?
Rewrites the cosine of a doubled angle using squared sine and cosine.
Can I copy this formula as LaTeX?
Yes. Copy \cos(2\theta)=\cos^2\theta-\sin^2\theta or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.