# Solving Pythagorean Identities

The Pythagorean identities in trigonometry are the three identities that come from the Pythagorean theorem.

Recall that the Pythagorean theorem states that the hypotenuse squared of a right triangle is the sum of the square of each of the other two sides.

a^{2} + b^{2} = c^{2}

Where c stands for the hypotenuse, and a and b are other two sides of the right triangle.

From this theorem, three identities can be determined from substituting in sine and cosine as follows:

sin^{2} θ + cos^{2} θ = 1

tan^{2} θ + 1 = sec^{2} θ

1 + cot^{2} θ = cosec^{2} θ