sin^4(3π/8)-cos^4(3π/8)=
[sin^2(3π/8)+cos^2(3π/8)]*[sin^2(3π/8)-cos^2(3π/8)]
=1*[sin^2(3π/8)-cos^2(3π/8)]
=[sin^2(3π/8)-cos^2(3π/8)]
=-[cos^2(3π/8)-sin^2(3π/8)]
=-[cos(2*3π/8)]
=-cos(3π/4)
=+cos(π/4)
=√2/2