Pythagorean identities are important equations in trigonometry that come from the Pythagorean theorem.

These equations show the relationships between sine, cosine, and tangent functions.

Here are the most common ones:

1. ( \text{sin}^2(x) + \text{cos}^2(x) = 1 )
2. ( 1 + \text{tan}^2(x) = \text{sec}^2(x) )
3. ( 1 + \text{cot}^2(x) = \text{csc}^2(x) )

These identities are really useful because they help us simplify expressions, solve equations, and prove other identities.

For example, if you know ( \text{sin}(x) ), you can easily find ( \text{cos}(x) ) using the first identity.

This makes solving problems a lot easier!