Question
If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.
Solution
∵ the line makes angles α, β, γ with the axes
∴ cos2 α + cos2 β + cos2 γ = 1
∴ 1 – sin2 α + 1 – sin2 β + 1 – sin2 γ = 1 or – sin2 α – sin2 β – sin2 γ = –2
∴ sin2 α + sin2 β + sin2 γ = 2.
