If α,β,γ are the angles which a line makes with the positive direction of coordinate axes, then the value of cos2α−sin2β+cos2γ=

If $α, β, γ$ are the angles which a line makes with the positive direction of coordinate axes, then the value of $\cos^{2} α - \sin^{2} β + \cos^{2} γ =$

A
0
B
1
C
2
D
3

Solution:

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 $\cos^{2} α + 1 - \sin^{2} β + \cos^{2} γ = 1 \Rightarrow \cos^{2} α - \sin^{2} β + \cos^{2} γ = 0$

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