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