A line makes angles α,β,γ with positive axes, then the range of ∑sinαsinβ is

If α,β,γ are the angles made by a line ‘L’ with the coordinate axes in the positive direction then cos2α+cos2β+cos2γ=1 and sin2α+sin2β+sin2γ=2Consider,∑sinα−sinβ2It implies that ∑sinα−sinβ2≥0∑sin2α+sin2β−2sinαsinβ≥02+2−2∑sinαsinβ≥0This gives ∑sinαsinβ≤2