已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,
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已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,
已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,
已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,
已知向量a=(cos3/2x,sin3/2x),b=(cosx/2,-sinx/2),x∈[0,π、2],求a.b,|a+b|
a.b
=(cos3x/2,sin3x/2).(cosx/2,-sinx/2)
=(cos3x/2)(cosx/2)-(sin3x/2)(sinx/2)
=cos2x
(a+b) = (cos3x/2+cosx/2,sin3x/2-sinx/2)
|a+b|^2 = (cos3x/2+cosx/2)^2+(sin3x/2-sinx/2)^2
= 2 + 2(cos3x/2cosx/2-sin3x/2sinx/2)
= 2 + 2cos2x
= 4(cosx)^2
|a+b| = 2cosx