If a line in the space makes angle $ \alpha, \beta $ and $ \gamma $ with the coordinate axes, then $ \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma $ equals

Question

If a line in the space makes angle $ \alpha, \beta $ and $ \gamma $ with the coordinate axes, then $ \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+\sin ^{2} \alpha+\sin ^{2} \beta+\sin ^{2} \gamma $ equals, $ -1 $, $ 0 $, $ 1 $, $ 2 $

MARKS App · Accepted Answer

cos ⁡ 2 α + cos ⁡ 2 β + cos ⁡ 2 γ + sin 2 ⁡ α + s i n 2 β + s i n 2 γ = c o s 2 α - s i n 2 α + c o s 2 β - s i n 2 β + c o s 2 γ - s i n 2 γ + sin 2 ⁡ α + s i n 2 β + s i n 2 γ = cos 2 ⁡ α + c o s 2 β + c o s 2 γ = 1

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