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Question

If a straight line makes angles α,β,γ with the x,y,z axes respectively, then show that sin2α+sin2β+sin2γ=2

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Solution

A] The line makes α,β,γ angles with x , y , z
axes
cos2α+cos2β+cos2γ=1
=1sin2α+1sin2β+1sin2γ=1
=sin2αsin2βsin2γ=11
=sin2α+sin2β+sin2γ=2

1181627_1291845_ans_82cc98f839b7416eb03b8094cab909ab.jpg

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