We know that if A({x}_{1},{y}_{1})&B({x}_{2},{y}_{2}) lies on the same side to line L=0, then LA(x1,y1)LB(x2,y2)>0.
Given, the points A(1,2)&B(\mathrm{sin}\theta ,\mathrm{cos}\theta ) lies on the same side of the line x+y−1=0.
∴(1+2−1)(sinθ+cosθ−1)>0
⇒sinθ+cosθ>1
⇒sinθ×21+cosθ×21>1×21
⇒sinθ.cos4π+cosθ.sin4π>21
⇒sin(θ+4π)>21
⇒4π<(θ+4π)<43π
⇒0<θ<2π
⇒θ∈(0,2π)