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Question
If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin2α + sin2β + sin2γ will be ______.
Options
1
3
–2
2
Solution
If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin2α + sin2β + sin2γ will be 2.
Explanation:
cos2α + cos2β + cos2γ = 1
`\implies` 1 – sin2α + 1 – sin2β + 1 – sin2γ = 1
`\implies` 3 – (sin2α + sin2β + sin2γ) = 1
`\implies` sin2α + sin2β + sin2γ = 2
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