已知tanα、tanβ是一元二次方程x^2+3x-3=0的两个根则sin^2(α+β)-4sin(α+β)cos(α+β)-2cos^2(α+β)=我知道tan(α+β)的值怎么算,就是想知道后面那个要求的有什么简便的方法算么
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![已知tanα、tanβ是一元二次方程x^2+3x-3=0的两个根则sin^2(α+β)-4sin(α+β)cos(α+β)-2cos^2(α+β)=我知道tan(α+β)的值怎么算,就是想知道后面那个要求的有什么简便的方法算么](/uploads/image/z/2095162-34-2.jpg?t=%E5%B7%B2%E7%9F%A5tan%CE%B1%E3%80%81tan%CE%B2%E6%98%AF%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bx%5E2%2B3x-3%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%E5%88%99sin%5E2%28%CE%B1%2B%CE%B2%29-4sin%28%CE%B1%2B%CE%B2%29cos%28%CE%B1%2B%CE%B2%29-2cos%5E2%28%CE%B1%2B%CE%B2%29%3D%E6%88%91%E7%9F%A5%E9%81%93tan%28%CE%B1%2B%CE%B2%29%E7%9A%84%E5%80%BC%E6%80%8E%E4%B9%88%E7%AE%97%EF%BC%8C%E5%B0%B1%E6%98%AF%E6%83%B3%E7%9F%A5%E9%81%93%E5%90%8E%E9%9D%A2%E9%82%A3%E4%B8%AA%E8%A6%81%E6%B1%82%E7%9A%84%E6%9C%89%E4%BB%80%E4%B9%88%E7%AE%80%E4%BE%BF%E7%9A%84%E6%96%B9%E6%B3%95%E7%AE%97%E4%B9%88)
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