Calculate (sin130)^2 + (cos50)^2.

It is obvious that sin 130 = sin
50.

We'll prove that using the
formula:

sin (a-b) = sin a * cos b - sin b* cos
a

We'll put a = 180 and b =
130

sin(180-50) = sin 130 = sin 180*cos 50 - sin 50 * cos
180

But sin 180 = 0 and cos 180 =
-1

sin(180-50) = 0 - (- sin
50)

sin 130 = sin 50

We'll
substitute sin 130 by sin 50 and we'll
get:

(sin 50)^2 + (cos 50)^2  =
1 (fundamental formula of trigonometry)