If a line makes angle α, β and γ with the axes respectively, then cos 2α + cos 2β + cos 2γ =

If a line makes angles α , β and γ with the axes then,

cos²α + cos²β + cos²γ = 1 → (1)

We have,

Cos2α + cos2β + cos2γ = 2cos²α – 1 + 2cos²β – 1 + 2cos²γ – 1 → (cos2θ = 2cos²θ -1)

= 2(cos²α + 2cos²β + 2cos²γ) – 3

= 2(1) – 3 → From (1)

= 2 – 3

= -1