l a x b l^2 + (a dot b)^2 = lal^2 lbl^2

a and b are vectors

well i know that a cross b = lallblsin theta and a dot b = lallblcos theta but i don't know how to proceed from here...

how would i go about proving this using the definitions of a cross b and a dot b? why is this equation equivalent to the Pythagorean identity?