sin^4(π/8)+cos^4(π/8)=( sin^2(π/8)+cos^2(π/8) )^2-2sin^2(π/8)+cos^2(π/8)=1-2sin^2(π/8)cos^2(π/8)=1-1/2 ( 4sin^2(π/8)cos^2(π/8))=1-1/2 ( sin2*(π/8))^2=1-1/2 *1/2=3/4