Basic trigonometric identities?

Basic trigonometric identity: sin ² α + cos ² α = 1.

It is a consequence of the Pythagorean theorem.

The Pythagorean theorem is one of the fundamental theorems of Euclidean geometry, which establishes the relationship between the sides of a right triangle: the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Let a and b be legs, c – hypotenuse.

sin² α = a / c,

cos ² α = b / c,

(a / c) ^ 2 + (b / c) ^ 2 = 1,

(a ^ 2 + b ^ 2) / c ^ 2 = 1,

a ^ 2 + b ^ 2 = c ^ 2.