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 :

Question

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 :, ( π 3 , π 2 ], ( 0 , π 4 ], π 4 , π 2, π 6 , π 3

MARKS App · Accepted Answer

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

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