α是第二象限角,sinα=1/4
cosα=-根号(1-sin^2α）=-根号(1-1/16)=-根号17/4
sin(α+π/4)=sinαcosπ/4+cosαsinπ/4=根号2/2(1/4-根号17)/4=-根号2(根号17 -1) /8
sin2α=2sinαcosα=2*1/4*（-根号17/4) = -根号17 /8
cos2α=1-2sin^2α=1-2*1/16=7/8
sin(α+π/4)/(sin2α+cos2α+1)
=[ -根号2(根号17 -1) /8 ] / [ -根号17 /8 + 7/8 +1]
=[ -根号2(根号17 -1)] / [ -根号17 + 7 +8]
=[ -根号2(根号17 -1)] / [15 -根号17 ]
=[ -根号2(根号17 -1) （15 -根号17)] / [15^2 -17 ]
=[ -根号2(16根号17 -32)] / 208
=[ -根号2(根号17 -2)] / 13
= (2根号2-根号34) / 13