∵cosx=-4/5,x∈(π/2,π)
∴sinx>0
sinx=√[1-(cosx)^2]=3/5
∴tanx=sinx/cosx=-3/4
∴tan(π/4-x)
=(tanπ/4-tanx)/(1+tanπ/4tanx)
=(1+3/4)/(1-3/4)
=(4+3)/(4-3)
=7