sina=-4/5,且a为第四象限角,故cosa>0,
由(sina)^2+(cosa)^2=1,可解得cosa=3/5,
故sin(2a- π/4)=sin2a *cosπ/4 - cos2a *sinπ/4
√2sin(2a-π/4)=sin2a-cos2a
而sin2a=2sina*cosa= -24/25,cos2a=2(cosa)^2 -1= -7/25
所以√2sin(2a-π/4)=sin2a-cos2a= -17/25
故原式=(1-√2sin(2a-π/4)/cosa
=(1+17/25)/(3/5)
=14/5