(sina/2+cosa/2)^2+2sin^2(π/4-a/2)=

(sina/2+cosa/2)²+2sin²(π/4-a/2)=sin²a/2+cos²a/2+2sina/2cosa/2+2sin²(π/4-a/2)=1+sina+1-cos[2(π/4-a/2)]=2+sina-cos(π/2-a)=2+sina-sina=2