ab=√2cosx+√2sinx=8/5
得sinx+cosx=(4/5)√2
于是(sinx+cosx)^2=32/25
即1+2sinxcosx=32/25,得2sinxcosx=7/25
那么(sinx-cosx)^2=1-2sinxcosx=1-7/25=18/25
得sinx-cosx=±(3/5)√2
tan(x-π/4)=(tanx-1)/(tanx+1)=(sinx-cosx)/(sinx+cosx)
=[±(3/5)√2]/[(4/5)√2]
=±3/4