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

β=π2−αcos2α+cos2β+cos2γ=1⇒90°cosα+cosβ+cosγ2=cosα+sinα2

β=π2−αcos2α+cos2β+cos2γ=1⇒90°cosα+cosβ+cosγ2=cosα+sinα2

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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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$1 + \sin 2 α$

$1 + \cos 2 α$

$1 - \sin 2 α$

$1$

answer is A.

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$β = \frac{π}{2} - α$

$\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \Rightarrow 90 °$

${(\cos α + \cos β + \cos γ)}^{2} = {(\cos α + \sin α)}^{2}$

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