f(x)=sin2x+cos2x=√2sin(2x+π/4)
f(π/4)=√2sin(2*π/4+π/4)=√2*√2/2=1
0<α<π
π/4<α+π/4<5π/4
f(α/2)=√2sin(α+π/4)=√2/2
sin(α+π/4)=1/2
α+π/4=5π/6
α=7π/12=π/3+π/4
sinα=sinπ/3cosπ/4+cosπ/3sinπ/4=(√6+√2)/4