Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Trigonometric identities

Revision as of 06:11, 24 June 2006 by Solafidefarms (talk | contribs) (Angle Addition formulae, prosthaphaersis heading add)

Trigonometric identities are used to manipulate trig equations in certain ways. Here is a list of them:


Reciprocal Identities

Pythagorean Identities

  • $\displaystyle \sin^2x + \cos^2x = 1$
  • $\displaystyle 1 + \cot^2x = \csc^2x$
  • $\displaystyle \tan^2x + 1 = \sec^2x$

Angle Addition Identities

  • $\displaystyle \sin \theta \cos \gamma + \sin \gamma \cos \theta = \sin \left(\theta+\gamma\right)$
  • $\displaystyle \cos \theta \cos \gamma - \sin theta \sin gamma = \cos \left(\theta+\gamma\right)$
  • $\displaystyle \frac{\tan \theta + \tan gamma}{1-\tan\theta\tan\gamma}=\tan\left(\theta+\gamma\right)$

Even-Odd Identities

Prosthaphaersis Indentities

(Otherwise known as sum-to-product identities)

Other Identities

  • $|1-e^{i\theta}|=2\sin\frac{\theta}{2}$

This page is incomplete--if you know of a trigonometric identity, add it.

See also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Trigonometric_identities&oldid=4443"