A line makes angles 2 α , 2 β , 2 Y with positive directions of the co-ordinate axes ( x , y , z axes respectively), then cos α + cos β + cos γ has the value

Question

A line makes angles 2 α ​ , 2 β ​ , 2 Y ​ with positive directions of the co-ordinate axes ( x , y , z axes respectively), then cos α + cos β + cos γ has the value

TestHub · Accepted Answer

​ cos α + cos β + cos γ = 2 cos 2 2 α ​ − 1 + 2 cos 2 2 β ​ − 1 + 2 cos 2 2 γ ​ − 1 = 2 ( cos 2 2 α ​ + cos 2 2 β ​ + cos 2 2 γ ​ ) − 3 = 2 × 1 − 3 [ ∵ cos 2 2 α ​ + cos 2 2 β ​ + cos 2 2 γ ​ = 1 ] = − 1 ​

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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