The range of θ in the interval 0,π such that the points 3,5 and sinθ,cosθ lie on the same side of the line x+y−1=0 is

We have line x+y−1=0.Let Lx,y=x+y−1.∴    L3,5=3+5−1=7>0For point 3,5 and sinθ,cosθ to lie on the same side of line x+y−1=0, we must haveLcosθ,sinθ>0sinπ4+θ>12π4<π4+θ<3π40<θ<π2