Practice: Trigonometric Identities

A Pythagorean identity is an equation that relates the squares of the sine, cosine, and tangent functions. The most common Pythagorean identities are: 1. $$\tan^2x + 1 = \frac{1}{\text{cos}^2x}$$ 2. $$\text{sin}^2x + \text{cos}^2x = 1$$ 3. $$1 + \text{cot}^2x = \text{csc}^2x$$ .

The Pythagorean identity involving sine and cosine is: $$\text{sin}^2x + \text{cos}^2x = 1$$ .

The identity for $$\tan(-x)$$ is: $$\tan(-x) = -\tan(x)$$ .

The identity for $$\text{sin}(-x)$$ is: $$\text{sin}(-x) = -\text{sin}(x)$$ .

The identity for $$\text{cos}(-x)$$ is: $$\text{cos}(-x) = \text{cos}(x)$$ .

The identity for $$\text{cot}(-x)$$ is: $$\text{cot}(-x) = -\text{cot}(x)$$ .

The identity for $$\text{sec}(-x)$$ is: $$\text{sec}(-x) = \text{sec}(x)$$ .

The identity for $$\text{csc}(-x)$$ is: $$\text{csc}(-x) = -\text{csc}(x)$$ .

The double angle formula for cosine is: $$\text{cos}(2x) = \text{cos}^2(x) - \text{sin}^2(x)$$ .

The double angle formula for sine is: $$\text{sin}(2x) = 2\text{sin}(x)\text{cos}(x)$$ .