已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1 /3,求cosx的值。
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![已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1 /3,求cosx的值。](/uploads/image/z/12362861-29-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28cos1.5x%2Csin1.5x%29%2Cb%3D%28cos0.5x%2C-sin0.5x%29%2Cx%E2%88%88%E3%80%90-%CF%80%2F2%2C%CF%80%2F2%E3%80%91%2C%E8%8B%A5%7Ca%2Bb%7C%3D1%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28cos1.5x%2Csin1.5x%29%2Cb%3D%28cos0.5x%2C-sin0.5x%29%2Cx%E2%88%88%E3%80%90-%CF%80%2F2%2C%CF%80%2F2%E3%80%91%2C%E8%8B%A5%7Ca%2Bb%7C%3D1+%2F3%EF%BC%8C%E6%B1%82cosx%E7%9A%84%E5%80%BC%E3%80%82)
已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1 /3,求cosx的值。
已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1
已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1 /3,求cosx的值。
已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1已知向量a=(cos1.5x,sin1.5x),b=(cos0.5x,-sin0.5x),x∈【-π/2,π/2】,若|a+b|=1 /3,求cosx的值。
向量a+b
=(cos1.5x+cos0.5x,sin1.5x-sin0.5x)
=(cos[x+0.5x]+cos[x-0.5x],sin[x+0.5x]-sin[x-0.5x])
=(2cosxcos0.5x,2cosxsin0.5x)
=2cosx(cos0.5x,sin0.5x)
那么有:
|a+b|=2|cosx|√[cos²0.5x+sin²0.5x]=2|cosx|=1/3
所以:cosx=±1/6
题目不全
然后呢,没问题么
a+b
=(cos1.5x+cos0.5x,sin1.5x-sin0.5x)
=(cos[x+0.5x]+cos[x-0.5x],sin[x+0.5x]-sin[x-0.5x])
=(2cosxcos0.5x,2cosxsin0.5x)
=2cosx(cos0.5x,sin0.5x)
|a+b|=2|cosx|√[cos²0.5x+sin²0.5x]=2|cosx|=1/3
所以:cosx=±1/6