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A line makes angles $60 °, 60 °, 45 °$ and $θ$ with the four diagonals of a cube. Then $\sin^{2} θ =$

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Correct option is B

If a line makes angles α,β,γ,δ with the four diagonals of a cube thencos2α+cos2β+cos2γ+cos2δ=43Here given α=60°,β=60°,γ=45°and δ=θHence, cos260°+cos260°+cos245°+cos2δ=4314+14+12+cos2θ=43cos2θ=13Therefore, sin2θ=1−13=23

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A line makes angles 60°,60°,45° and θ with the four diagonals of a cube. Then sin2θ=

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Ready to Test Your Skills?

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A line makes angles $60 °, 60 °, 45 °$ and $θ$ with the four diagonals of a cube. Then $\sin^{2} θ =$