已知2sin²a-cos²a+sinacosa-6sina+3cosa=0,求2cos²a
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已知2sin²a-cos²a+sinacosa-6sina+3cosa=0,求2cos²a的值
![已知2sin²a-cos²a+sinacosa-6sina+3cosa=0,求2cos²a](/uploads/image/z/17720360-8-0.jpg?t=%E5%B7%B2%E7%9F%A52sin%26sup2%3Ba-cos%26sup2%3Ba%2Bsinacosa-6sina%2B3cosa%3D0%2C%E6%B1%822cos%26sup2%3Ba)
注:^2表示平方
2sin^2a-cos^2a+sinacosa-6sina+3cosa
=2sin^2a+sinacosa-cos^2a-6sina+3cosa
=(2sina-cosa)(sina+cosa)-3(2sina-cosa)
=(2sina-cosa)(sina+cosa-3)=0
2sina-cosa=0,或 sina+cosa=3 显然不成立
所以2sina-cosa=0
sina/cosa=tana=1/2
2cos^2a=1+cos2a
=1+(1-tan^2a)/(1+tan^2a)
=1+(1-1/4)/(1+1/4)
=8/5
2sin^2a-cos^2a+sinacosa-6sina+3cosa
=2sin^2a+sinacosa-cos^2a-6sina+3cosa
=(2sina-cosa)(sina+cosa)-3(2sina-cosa)
=(2sina-cosa)(sina+cosa-3)=0
2sina-cosa=0,或 sina+cosa=3 显然不成立
所以2sina-cosa=0
sina/cosa=tana=1/2
2cos^2a=1+cos2a
=1+(1-tan^2a)/(1+tan^2a)
=1+(1-1/4)/(1+1/4)
=8/5
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