The set of all possible values of θ in the interval 0 , π for which the points 1 , 2 and sin θ , cos θ lie on the same side of the line x + y = 1 is?

Step-by-step solution

We know that if A x 1 , y 1   &   B x 2 , y 2 lies on the same side to line L = 0 , then L A x 1 , y 1   L B x 2 , y 2 > 0 . Given, the points A 1 , 2   &   B sin θ , cos θ lies on the same side of the line x + y - 1 = 0 . ∴ 1 + 2 - 1 sin θ + cos θ - 1 > 0 ⇒ sin θ + cos θ > 1 ⇒ sin θ × 1 2 + cos θ × 1 2 > 1 × 1 2 ⇒ sin θ . cos π 4 + cos θ . sin π 4 > 1 2 ⇒ sin