>>237
cos(4x)
=1-2sin(2x)^2
=1-8(sin(x)cos(x))^2

ところでsin(x)cos(x)=((sin(x)+cos(x))^2-1)/2=(t^2-1)/2であるから
1-8(sin(x)cos(x))^2=1-8((t^2-1)/2)^2=-2t^4+4t^2-1