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sinα(sinα·sinα/cosα+cosα)=tgα ⇔ tgα=sinα/cosα
sinα(sin²α/cosα+cosα)=tgα
sinα(sin²α/cosα+cos²α/cosα)=tgα
sinα(sin²α+cos²α/cosα)=tgα ⇔ sin²α+cos²α=1
sinα·1/cosα=tgα
sinα/cosα=tgα