The direction angles made by a line ' L ’ with the coordinate axes, are α,β,γ. Then the range of sin2α+sin2β

If $α, β, γ$ are the angles made by a line ‘L’ with the coordinate axes in the positive direction then $\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$

It implies that $1 - \sin^{2} α + 1 - \sin^{2} β + 1 - \sin^{2} γ = 1 \Rightarrow \sin^{2} α + \sin^{2} β + \sin^{2} γ = 2$

Hence, $\sin^{2} α + \sin^{2} β = 2 - \sin^{2} γ$

The minimum value of $\sin^{2} γ$ is zero and its maximum value is 1

So that the range of $\sin^{2} α + \sin^{2} β$ is $[1, 2]$

The direction angles made by a line ' $L$ ’ with the coordinate axes, are $α, β, γ$ . Then the range of $\sin^{2} α + \sin^{2} β$