| Think of how the trigonometric functions are defined for a right-angled triangle.
Cos(theta) = adjacent/hypotenuse.
sin(theta) = opposite/hypotenuse.
sin^2 + cos^2 = o^2/h^2 + a^2/h^2
= (o^2 + a^2)/h^2
But, from the pythagorean theorem,
o^2 + a^2 = h^2
Therefore,
cos^2 + sin^2 = (o^2 + a^2)/h^2 = 1 |