若tanx=-2分之一,求2sin^2x+sinx乘cosx-3cos^x
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若tanx=-2分之一,求2sin^2x+sinx乘cosx-3cos^x
![若tanx=-2分之一,求2sin^2x+sinx乘cosx-3cos^x](/uploads/image/z/20016166-22-6.jpg?t=%E8%8B%A5tanx%3D-2%E5%88%86%E4%B9%8B%E4%B8%80%2C%E6%B1%822sin%5E2x%2Bsinx%E4%B9%98cosx-3cos%5Ex)
标准做法
2sin^2x+sinx乘cosx-3cos^x
=(2sin^2x+sinx乘cosx-3cos^x)/(sin²x+cos²x)
=(2tan²x+tanx-3)/(tan²x+1)
=(1/2-1/2-3)/(1/4+1)
=-12/5
2sin^2x+sinx乘cosx-3cos^x
=(2sin^2x+sinx乘cosx-3cos^x)/(sin²x+cos²x)
=(2tan²x+tanx-3)/(tan²x+1)
=(1/2-1/2-3)/(1/4+1)
=-12/5
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