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Question
If a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.
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Solution
If a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is 2.
Explanation:
Note that sin2α + sin2β + sin2γ = (1 – cos2α) + (1 – cos2β) + (1 – cos2γ)
= 3 – (cos2α + cos2β + cos2γ)
= 2.
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