已知a=(cos2a,sina),b=(1,2sina-1),a∈(π /2,π ),a*b=2/5.求[√2sin2a-4cos(a+π/4)]/[cos^2a/2]的值
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![已知a=(cos2a,sina),b=(1,2sina-1),a∈(π /2,π ),a*b=2/5.求[√2sin2a-4cos(a+π/4)]/[cos^2a/2]的值](/uploads/image/z/8740498-58-8.jpg?t=%E5%B7%B2%E7%9F%A5a%EF%BC%9D%28cos2a%2Csina%29%2Cb%EF%BC%9D%281%2C2sina-1%29%2Ca%E2%88%88%28%CF%80+%2F2%2C%CF%80+%29%2Ca%2Ab%3D2%2F5.%E6%B1%82%5B%E2%88%9A2sin2a-4cos%28a%2B%CF%80%2F4%29%5D%2F%5Bcos%5E2a%2F2%5D%E7%9A%84%E5%80%BC)
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已知a=(cos2a,sina),b=(1,2sina-1),a∈(π /2,π ),a*b=2/5.求[√2sin2a-4cos(a+π/4)]/[cos^2a/2]的值
已知a=(cos2a,sina),b=(1,2sina-1),a∈(π /2,π ),a*b=2/5.求[√2sin2a-4cos(a+π/4)]/[cos^2a/2]的值
已知a=(cos2a,sina),b=(1,2sina-1),a∈(π /2,π ),a*b=2/5.求[√2sin2a-4cos(a+π/4)]/[cos^2a/2]的值
A*B=cos 2a+(2sin a -1)sin a=cos 2a + 2sin² a - sin a = 1 - sin a (注意到cos 2a = 1 - 2sin² a).
又A*B=2/5,从而sin a =3/5
由于a∈[ π/2,π],因此cos a取负值,即cos a=-√(1 - sin² a) =-4/5
sin 2a = 2sin a*cos a = -3√91/50;
cos (a+π/4) = cos a*cos π/4 - sin a*sin π/4 = √2/2 (cos a - sin a) =……(三角函数和差化积公式)
cos² a/2 = 1 + cos a =……自己算
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