A line makes angles α,β,γ with the coordinate axes. If α+β=π2 then (cos⁡α+cos⁡β+cos⁡γ)2 is equal to

β=π2−α⇒cos2⁡α+cos2⁡β+cos2⁡γ=1cos2⁡α+sin2⁡α+cos2⁡γ=1⇒cos2⁡γ=0⇒γ=90∘,(cos⁡α+cos⁡β+cos⁡γ)2=(cos⁡α+sin⁡α)2=1+sin2α

A line makes angles α,β,γ with the coordinate axes. If α+β=π2 then (cos⁡α+cos⁡β+cos⁡γ)2 is equal to

β=π2−α⇒cos2⁡α+cos2⁡β+cos2⁡γ=1cos2⁡α+sin2⁡α+cos2⁡γ=1⇒cos2⁡γ=0⇒γ=90∘,(cos⁡α+cos⁡β+cos⁡γ)2=(cos⁡α+sin⁡α)2=1+sin2α

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A line makes angles $α, β, γ$ with the coordinate axes. If $α + β = \frac{π}{2}$ then $(\cos α + \cos β + \cos γ)^{2}$ is equal to

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$1 + \sin 2 α$

$1 - \sin 2 α$

$1 + \cos 2 α$

answer is A.

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Detailed Solution

$\begin{array}{l} β = \frac{π}{2} - α \Rightarrow \cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \\ \cos^{2} α + \sin^{2} α + \cos^{2} γ = 1 \Rightarrow \cos^{2} γ = 0 \\ \Rightarrow γ = 90^{\circ}, (\cos α + \cos β + \cos γ)^{2} = (\cos α + \sin α)^{2} = 1 + \sin 2 α \end{array}$