Question

If a line makes angles α, β, γ with the co-ordinate axes, prove that sin²α + sin²β + sinγ² = 2.

Answer 1

Since a line makes angles α, β, γ with the co-ordinate axes, 

hence cosα, cosβ, cosγ are its direction cosines 

∴ cos²α + cos²β + cos²γ = 1 

⇒ (1 – sin²α) + (1 – sin²β) + (1 – sin²γ) = 1 

⇒ sin²α + sin²β + sin²γ = 2.