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प्रश्न
Select the correct option from the given alternatives :
If α + β + γ = π then the value of sin2α + sin2β – sin2γ is equal to …......
पर्याय
2 sin α
2 sin α cos β sin γ
2 sin α sin β cos γ
2 sin α sin β sin γ
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उत्तर
2 sin α sin β cos γ
Explanation:
`sin^2alpha + sin^2 beta - sin^2γ`
= `(1 - cos2alpha)/2 + (1 - cos2beta)/2 - sin^2γ`
= `1 - 1/2(cos2alpha + cos2beta) - 1 + cos^2γ`
= `-1/2 xx 2cos(alpha + beta)cos(alpha - beta) + cos^2γ`
= cos γ cos (α – β) + cos2γ ...[∵ α + β + γ = π]
= cos γ [cos (α – β) + cos γ]
= cos γ [cos (α – β) – cos (α + β)]
= 2 sin α sin β cos γ
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