A line in the 3 -dimensional space makes an angle θ 0 < θ ≤ π 2 with both the X and Y - axes. Then, the set of all values of θ is in the interval :

Step-by-step solution

cos 2 α + cos 2 β + cos 2 γ = 1 α = β = θ ⇒ cos 2 γ + 2 cos 2 θ = 1 cos 2 γ = 1 - 2 cos 2 θ 0 ≤ cos 2 γ ≤ 1 0 ≤ 1 - 2 cos 2 θ ≤ 1 - 1 ≤ - 2 cos 2 θ ≤ 0 0 ≤ cos 2 θ ≤ 1 2 (as θ > 0 ,  cos θ < 1 ) ⇒    0 ≤ cos θ ≤ 1 2 π 4 ≤ θ ≤ π 2