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Question

If a line makes angle (α,β,γ) with the co-ordinates axes. Prove that sin2α+sin2βcos2γ=1

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Solution

l=cosαm=cosβn=cosγ
Now
l2+m2+n2=1cos2α+cos2β+cos2γ=11sin2α+1sin2β+cos2γ=12sin2αsin2β+cos2γ=1sin2α+sin2β+1cos2γ2=0sin2α+sin2βcos2γ1=0sin2α+sin2βcos2γ=1

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