Question

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sin(α-β)*cosβ+cos(α-β)*sinβ / cos(α-β)*cosβ-sin(α-β)sinβ = tgα

Answer 1

(sin(α-β)*cosβ+cos(α-β)*sinβ) / (cos(α-β)*cosβ-sin(α-β)sinβ) =

(sin(α-β+β))/(cos(α-β+β))=sinα/cosα=tgα