Table of Trigonometric Identities

# Table of Trigonometric Identities

A few of the more common trigonometric identities are given below.

## Pythagorean Identities

- $\sin^2 x + \cos^2 x = 1$.

- $1 + \tan^2 x = \sec^2 x$.

- $1 + \cot^2 x = \csc^2 x$.

## Even/Odd Identities

- $\sin (-x) = - \sin x$.

- $\cos (-x) = \cos x$.

- $\tan (-x) = -\tan x$.

## Double Angle Identities

- $\sin (2x) = 2 \sin x \cos x$.

- $\cos (2x) = \cos^2 x - \sin^2 x = 2 \cos^2 x - 1 = 1 - 2 \sin^2 x$.

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

## Sum and Difference Identities

- $\sin (x + y) = \sin x \cos y + \cos x \sin y$.

- $\sin (x - y) = \sin x \cos y - \cos x \sin y$.

- $\cos (x + y) = \cos x \cos y - \sin x \sin y$.

- $\cos (x - y) = \cos x \cos y + \sin x \sin y$.

## Reduction Identities

- $\sin^2 x = \frac{1 - \cos 2x}{2}$.

- $\cos^2 x = \frac{1 + \cos 2x}{2}$.