If a line in 3 dimensions makes angles α, β and γ with the positive directions of the coordinate axes, then what is cos(α+β)cos(α-β) equal to?

Question

Accepted Answer

-cos²γ. cos(α+β)cos(α-β) = cos²α - sin²β. Using cos²α + cos²β + cos²γ = 1: cos²α = 1 - cos²β - cos²γ. So cos²α - sin²β = 1 - cos²β - cos²γ - (1-cos²β) = -cos²γ.

If a line in 3 dimensions makes angles α, β and γ with the positive directions of the coordinate axes, then what is cos(α+β)cos(α-β) equal to?

Explanation

More 3D Geometry / Direction Cosines questions

Want more NDA practice?