Hi my first post! Feel embarrassed I cant see the solution as I though I was getting quite good at these.... Any here is the question:

If a2 + b2 = 1 = c2 + d2 ; a, b, c, d are elements of R

Prove that ab + cd<1

Apologies I cant seem to use superscript; the number 2 in the question is meant to be to the power of 2 for each of the letters in the equation.