Each of the angles β and γ that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive x -axes. Then the sum of all possible va

Question

Each of the angles β and γ that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive x -axes. Then the sum of all possible values of the angle β is

TestHub · Accepted Answer

​ β = 2 α ​ , γ = 2 α ​ cos 2 α + cos 2 β + cos 2 γ = 1 cos 2 α + 2 cos 2 2 α ​ = 1 cos 2 α + cos α = 0 cos α ( cos α + 1 ) = 0 cos α = 0 , − 1 α = 2 π ​ , π ​ Now β = 2 α ​ ⇒ 4 π ​ , 2 π ​ so sum is 4 3 π ​

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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