Question

4m=cotA(1+SinA), 4n=cotA(1-SinA)
Proved that
(m2-n2)=mn

Answer 1

There must be a typo. Plug in A = pi/4 and you have

4m = (1 + 1/√2), so m = (2+√2)/8
4n = (1 - 1/√2), so n = (2-√2)/8
m2-n^2 = √2/8

mn = 1/32