A line makes the same angle ' α ' with each of the x and y axes. If the angle ' θ ', which it makes with the z-axis, is such that sin 2 θ = 2 sin 2 α , then the angle α is

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Direction cosines of the line are cos 2 α + cos 2 α + cos 2 θ = 1 ​ ⇒ cos 2 α + cos 2 α + 1 − sin 2 θ = 1 ⇒ cos 2 α + cos 2 α + 1 − 2 sin 2 α = 1 ⇒ 1 − sin 2 α + 1 − sin 2 α + 1 − 2 sin 2 α = 1 ⇒ sin 2 α = 2 1 ​ = sin 2 4 π ​ ⇒ α = 4 π ​ ​

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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