sinē x + cosē x = 1

Let us consider a right angled triangle ABC with AB, BC and AC
respectively as the altitude, base and the hypotenuse, where
< ABC = 90 degrees.

Then, AB^2 + BC^2 = AC^2
Or, (AB/AC)^2 + (BC/AC)^2 = 1........(*)

We know that:

sin x = altitude/ hypotenuse = AB/ AC
cos x = base/ hypotenuse = BC/AC

Thus, from (*) we obtain:

sin^2(x) + cos^2(x) = 1