a-maths~~~~~~~~~~~

sinθ+cosθ=m
(sinθ+cosθ)^2=m^2
1+2sinθcosθ=m^2
sin2θ=m^2-1
cos2θ=n
therefore
[m^2-1]^2 + n^2=1
m^4-2m^2 + 1 + n^2 =1
m^4-2m^2 + n^2 = 0
x=cotθ+cosθ
y=cotθ-cosθ
16xy =16 (cotθ+cosθ)(cotθ-cosθ)
=16(cotθ)^2 - (cosθ)^2
=16(cosθ)^2[ 1/((sinθ)^2) - 1]
=16(cotθ)^2[ 1 - (sinθ)^2]
=16(cotθ)^2 (cosθ)^2
(x2-y2)
=(cotθ+cosθ)2 - (cotθ-cosθ)2
=(cotθ+cosθ+cotθ-cosθ )(cotθ+cosθ-cotθ+cosθ )
=(2cotθ)(2cosθ)
=4cotθcosθ
(x2-y2)2
=16(cotθ)^2 (cosθ)^2
=16xy