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ابو الوفاء بوزجانی
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ابو الوفاء بوزجانی. Sin( α + β )=Sin α .Cos β +Cos α .Sin β. لم:. در دایره ای به شعاع 1:. α. α. مشاهده می شود که وتر رو به رو به زاویه α 2 ، برابر 2Sin α است. B. A. E. C. BE = 2.Sin α. α. α. β. F. BF = 2.Sin β. β. O. EF = 2.Sin( α + β ). <BEF = β. <BFE = α. B.
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ابو الوفاء بوزجانی
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ابو الوفاء بوزجانی Sin(α+β)=Sin α.Cos β +Cos α.Sin β
لم: در دایره ای به شعاع 1: α α مشاهده می شود که وتر رو به رو به زاویه α2 ، برابر2Sinαاست.
B A E C BE = 2.Sinα α α β F BF = 2.Sinβ β O EF = 2.Sin(α+β) <BEF = β <BFE = α
B FH = BF.Cosα= 2.Sinβ.Cosα E β α H EH = BE.Cosβ = 2.Sinα.Cosβ F FH + EH=EF => 2.Sin(α+β) = 2.Sinα.Cosβ +2.Cosα.Sinβ => Sin(α+β) = Sinα.Cosβ+Cosα.Sinβ
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