A Math Question

sin 15/cos 15 + cos 15/sin 15 = (sin² 15 + cos² 15)/(sin 15 cos 15) = 1/(sin 15 cos 15) = 2/(sin 30) (double angle formula) = 4.

Prove this result without using any trig.  (Label the legs of a 15-75-90 triangle x and y.  Show x/y + y/x = 4.)