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.

a2 + b2 = c2

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:

sin2 θ + cos2 θ = 1

tan2 θ + 1 = sec2 θ

1 + cot2 θ = cosec2 θ

👉 Proof of Pythagorean Identities