consider

in this figure, we have that NOPR is a rectangle, ON was extended and we get the point M. Join M and P and extend NR, point Q borns. Finally make QP orthogonal to MP and join M and Q.

let and It's easy to prove that

compute and we have it's equal to Multiply the first quotient top and bottom by and in the same fashion for the second quotient by and you'll get the identity.