已知tana=2,则sin^2a+sina*cosa-2cos^2a=

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tana = 2
sin²a = 4/5
cos²a = 1/5
sina cosa = 2/5
sin²a + sina cosa - 2cos²a = 4/5 + 2/5 - 2/5 = 4/5
再问： sina,cosa怎么推出来的？求方法
再答： tan²a = sin²a / (1 - sin²a) = 4 , sin²a = 4/5 cos²a = 1 - sin²a = 1/5 (sina cosa)² = sin²a cos²a = 4/25 tana = sina / cosa > 0 sina cosa > 0 sina cosa = 2/5 sin²a + sina cosa - 2cos²a = 4/5 + 2/5 - 2/5 = 4/5
再问：大神，这里不明白，麻烦再教我一下tan²a = sin²a / (1 - sin²a) = 4
再答： tana = sina / cosa tan²a = sin²a / cos²a = sin²a / (1 - sin²a) sin²a = tan²t / (1 + tna²t) = 4/5
再问：谢谢，大神，你说的我都明白了，可是sin²a = tan²t / (1 + tna²t) = 4/5是不是你打错了，我怎么弄给出这一步啊
再答：应该是：sin²a = tan²a / (1 + tna²a) = 4/5 推导过程如下：tana = sina / cosa tan²a = sin²a / cos²a = sin²a / (1 - sin²a)tan²a(1 - sin²a) = sin²atan²a - tan²a sin²a = sin²atan²a = (tan²a + 1)sin²asin²a = tan²a / (1 + tan²a)

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