已知向量m=(根号3sinx/4,1),向量n=(cosx/4,cos^2 x/4) 若向量m垂直向量n,求cos(2π/3-X)
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![已知向量m=(根号3sinx/4,1),向量n=(cosx/4,cos^2 x/4) 若向量m垂直向量n,求cos(2π/3-X)](/uploads/image/z/616480-16-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fm%3D%28%E6%A0%B9%E5%8F%B73sinx%2F4%2C1%29%2C%E5%90%91%E9%87%8Fn%3D%28cosx%2F4%2Ccos%5E2+x%2F4%29+%E8%8B%A5%E5%90%91%E9%87%8Fm%E5%9E%82%E7%9B%B4%E5%90%91%E9%87%8Fn%2C%E6%B1%82cos%282%CF%80%2F3-X%29)
已知向量m=(根号3sinx/4,1),向量n=(cosx/4,cos^2 x/4) 若向量m垂直向量n,求cos(2π/3-X)
已知向量m=(根号3sinx/4,1),向量n=(cosx/4,cos^2 x/4) 若向量m垂直向量n,求cos(2π/3-X)
已知向量m=(根号3sinx/4,1),向量n=(cosx/4,cos^2 x/4) 若向量m垂直向量n,求cos(2π/3-X)
m•n=√3sin(x/4)cos(x/4)+cos²(x/4)
=(√3/2)sin(x/2)+(1/2)cos(x/2)+1/2
=cos(x/2-π/3)+1/2
因为向量m垂直向量n,所以cos(x/2-π/3)+1/2=0,
cos(x/2-π/3)=-1/2
所以cos(2π/3-X)=cos(x-2π/3)
= cos2(x/2-π/3)=2 cos²(x/2-π/3)-1
=-1/2.