If a line in the space makes angles α, β and γ with the coordinate axes, then cos 2 α+ cos 2 β+ cos 2 γ+ sin 2 α+ sin 2 β+ sin 2 γ=

Question

If a line in the space makes angles α, β and &gamma; with the coordinate axes, then cos 2 α+ cos 2 β+ cos 2 &gamma;+ sin 2 α+ sin 2 β+ sin 2 &gamma;= (A) -1 (B) 0 (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

cos 2 α+ cos 2 β+ cos 2 &gamma;+ sin 2 α+ sin 2 β+ sin 2 &gamma; =2 cos 2 α-1+2 cos 2 β-1+2 cos 2 &gamma;-1+1- cos 2 α+1- cos 2 β+1- cos 2 &gamma; = cos 2 α+ cos 2 β+ cos 2 &gamma;=1

Q. If a line in the space makes angles $α, β$ and $γ$ with the coordinate axes, then $cos 2 α + cos 2 β + cos 2 γ + sin^{2} α + sin^{2} β + sin^{2} γ =$

$- 1$

0

1

2

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

Q. If a line in the space makes angles α,β and γ with the coordinate axes, then cos2α+cos2β+cos2γ+sin2α+sin2β+sin2γ=

−1

0

1

2

cos2α+cos2β+cos2γ+sin2α+sin2β+sin2γ =2cos2α−1+2cos2β−1+2cos2γ−1+1−cos2α+1−cos2β+1−cos2γ =cos2α+cos2β+cos2γ=1

Q. If a line in the space makes angles $α, β$ and $γ$ with the coordinate axes, then $cos 2 α + cos 2 β + cos 2 γ + sin^{2} α + sin^{2} β + sin^{2} γ =$

$- 1$

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