证明下列恒等式成立; (1)tan^2α-sin^2α=tan^2α*sin^2α (2)tan*(1-cot^2α)+cot*(1-tan^2α)=0; (3)(sinα-cosα)^2=1-2sinαcosα; (4)(tanα+tanβ)/(cotα+cotβ)=tanα*tanβ
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![证明下列恒等式成立; (1)tan^2α-sin^2α=tan^2α*sin^2α (2)tan*(1-cot^2α)+cot*(1-tan^2α)=0; (3)(sinα-cosα)^2=1-2sinαcosα; (4)(tanα+tanβ)/(cotα+cotβ)=tanα*tanβ](/uploads/image/z/6884835-51-5.jpg?t=%E8%AF%81%E6%98%8E%E4%B8%8B%E5%88%97%E6%81%92%E7%AD%89%E5%BC%8F%E6%88%90%E7%AB%8B%EF%BC%9B+%EF%BC%881%EF%BC%89tan%5E2%CE%B1-sin%5E2%CE%B1%3Dtan%5E2%CE%B1%2Asin%5E2%CE%B1+%EF%BC%882%EF%BC%89tan%2A%281-cot%5E2%CE%B1%EF%BC%89%2Bcot%2A%281-tan%5E2%CE%B1%EF%BC%89%3D0%EF%BC%9B+%EF%BC%883%EF%BC%89%EF%BC%88sin%CE%B1-cos%CE%B1%EF%BC%89%5E2%3D1-2sin%CE%B1cos%CE%B1%EF%BC%9B+%EF%BC%884%EF%BC%89%EF%BC%88tan%CE%B1%2Btan%CE%B2%EF%BC%89%2F%EF%BC%88cot%CE%B1%2Bcot%CE%B2%EF%BC%89%3Dtan%CE%B1%2Atan%CE%B2)
证明下列恒等式成立; (1)tan^2α-sin^2α=tan^2α*sin^2α (2)tan*(1-cot^2α)+cot*(1-tan^2α)=0; (3)(sinα-cosα)^2=1-2sinαcosα; (4)(tanα+tanβ)/(cotα+cotβ)=tanα*tanβ
证明下列恒等式成立; (1)tan^2α-sin^2α=tan^2α*sin^2α (2)tan*(1-cot^2α)+cot*(1-tan^2α)=0; (3)(sinα-cosα)^2=1-2sinαcosα; (4)(tanα+tanβ)/(cotα+cotβ)=tanα*tanβ
证明下列恒等式成立; (1)tan^2α-sin^2α=tan^2α*sin^2α (2)tan*(1-cot^2α)+cot*(1-tan^2α)=0; (3)(sinα-cosα)^2=1-2sinαcosα; (4)(tanα+tanβ)/(cotα+cotβ)=tanα*tanβ
1)sina=tana×cosa tana-sina=tana-tana×cosa=tana(1-cosa)=tanasina 2)tanacota=1 tana(1-cota)+cota(1-tana)=tana-tanacota+cota-tanacota=(tana+cota)-tanacota(tana+cota) =(tana+cota)(1-tanacota)=(tana+cota)×0=0 3)(sina-cosa)=sina+cosa-2sinacosa=1-2sinacosa 4)cota=1/tana,cotb=1/tanb (tana+tanb)/(cota+cotb)=(tana+tanb)/(1/tana+1/tanb)=(tana+tanb)[(tana+tanb)/tanatanb]=tanatanb