The range of θ  in (0,π)  such that the point (3,5) and (sinθ,cosθ)  lie on the same side of the line x + y – 1 = 0 is

3+5−1>0 sinθ+cosθ>1   (divide with 2)sin(θ+π4)>12=sinπ4 The points A,B are on same side of a line L≡0 then LA, LB have same sign⇒θ+π4∈(π4,3π4)⇒θ∈(0,π2)