If α ,β ,γ are the angles when a directed line makes with the positive directions the coordinate axes, then sin 2α + sin 2β + sin 2γ is equal to:

Question

If α ,β ,&gamma; are the angles when a directed line makes with the positive directions the coordinate axes, then sin 2α + sin 2β + sin 2&gamma; is equal to: (A) 1 (B) 2 (C) 3 (D) none of these

Tardigrade Admin · Accepted Answer

If the line makes an angle α, β, &gamma; to the coordinate axes, then cos 2 α+ cos 2 β+ cos 2 &gamma;=1 We know that cos 2 α+ cos 2 β+ cos 2 &gamma;=1 ⇒ 1- sin 2 α+1- sin 2 β+1- sin 2 &gamma;=1 ⇒ sin 2 α+ sin 2 β+ sin 2 &gamma;=3-1 =2

Q. If $α, β, γ$ are the angles when a directed line makes with the positive directions the coordinate axes, then $sin^{2} α + sin^{2} β + sin^{2} γ$ is equal to:

1

2

3

none of these

If the line makes an angle $α, β, γ$ to the coordinate axes, then
$cos^{2} α + cos^{2} β + cos^{2} γ = 1$
We know that $cos^{2} α + cos^{2} β + cos^{2} γ = 1$
$\Rightarrow 1 - sin^{2} α + 1 - sin^{2} β + 1 - sin^{2} γ = 1$
$\Rightarrow sin^{2} α + sin^{2} β + sin^{2} γ = 3 - 1$
$= 2$

Q. If α,β,γ are the angles when a directed line makes with the positive directions the coordinate axes, then sin2α+sin2β+sin2γ is equal to:

1

2

3

none of these

If the line makes an angle α,β,γ to the coordinate axes, then cos2α+cos2β+cos2γ=1 We know that cos2α+cos2β+cos2γ=1 ⇒1−sin2α+1−sin2β+1−sin2γ=1 ⇒sin2α+sin2β+sin2γ=3−1 =2

Q. If $α, β, γ$ are the angles when a directed line makes with the positive directions the coordinate axes, then $sin^{2} α + sin^{2} β + sin^{2} γ$ is equal to:

If the line makes an angle $α, β, γ$ to the coordinate axes, then
$cos^{2} α + cos^{2} β + cos^{2} γ = 1$
We know that $cos^{2} α + cos^{2} β + cos^{2} γ = 1$
$\Rightarrow 1 - sin^{2} α + 1 - sin^{2} β + 1 - sin^{2} γ = 1$
$\Rightarrow sin^{2} α + sin^{2} β + sin^{2} γ = 3 - 1$
$= 2$