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