Question

A line makes angles α, β, γ with the positive directions of coordinate axes, then find the value of sin²α + sin²β + sin²γ.

Answer 1

We have : cos²α + cos²β + cos²γ = 1

∴ 1 – sin²α + 1 – sin²β + 1 – sin²γ = 1

∴ 3 – sin²α – sin²β – sin²γ = 1

∴ sin²α + sin²β + sin²γ = 2