Geometry Quiz
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TRIGONOMETRIC IDENTITIES
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Which reasoning supports the angle addition formula? In the diagram, triangle ABCABC has point DD on segment ACAC. At vertex AA, ray ADAD splits ∠BAC\angle BAC into two angles labeled θ\theta (between ABAB and ADAD) and φ\varphi (between ADAD and ACAC), so ∠BAC=θ+φ\angle BAC=\theta+\varphi. Segment BDBD is drawn. A right-angle marker indicates BD⊥ACBD\perp AC at DD. Which statement proves an identity for sin⁡(θ+φ)\sin(\theta+\varphi) using this construction? Figure accompanying this question
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