已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),且x属于[π/2,π],.|a+b|大于根号3,求x的取值范围
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![已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),且x属于[π/2,π],.|a+b|大于根号3,求x的取值范围](/uploads/image/z/7645792-40-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28cos3%2F2x%2Csin3%2F2x%29%2Cb%3D%28cosx%2F2%2C-sinx%2F2%29%2C%E4%B8%94x%E5%B1%9E%E4%BA%8E%5B%CF%80%2F2%2C%CF%80%5D%2C.%7Ca%2Bb%7C%E5%A4%A7%E4%BA%8E%E6%A0%B9%E5%8F%B73%2C%E6%B1%82x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),且x属于[π/2,π],.|a+b|大于根号3,求x的取值范围
已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),且x属于[π/2,π],.|a+b|大于根号3,求x的取值范围
已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),且x属于[π/2,π],.|a+b|大于根号3,求x的取值范围
a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),|a+b|>√3,
∴(a+b)^2=(cos3/2x+cosx/2)^2+(sin3/2x-sinx/2)^2
=2+2(cos3/2xcosx/2-sin3/2xsinx/2)
=2+2cos2x>3,
∴cos2x>1/2,
x∈[π/2,π],
∴2x∈[π,2π],
∴5π/3