若cos2x/sin(x－派/4)=－√2/2,则cosx＋sinx的值为?

若cos2x/sin(x－派/4)=－√2/2,则cosx＋sinx的值为?
若cos2x/sin(x－派/4)=－√2/2,则cosx＋sinx的值为?

若cos2x/sin(x－派/4)=－√2/2,则cosx＋sinx的值为?
(cos²x-sin²x)/(sinxcosπ/4-cosxsinπ/4)=-√2/2
(cosx+sinx)(cosx-sinx)/[-√2/2(cosx-sinx)]=-√2/2
所以cosx+sinx=1/2

lgx+lgy=lgxy=lg(x+y)
所以xy=x+y
xy-x-y+1=1
(1-x)(1-y)=1
所以原式=lg[(1-x)(1-y)]
=lg1
=0