a=(1,sin^2(x)),b=(2,sin2x),其中x属于(0,派),若|向量a·向量b|=|向量a||向量b|,则tanx的值为?

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a=(1,sin^2(x)),b=(2,sin2x),其中x属于(0,派),若|向量a·向量b|=|向量a||向量b|,则tanx的值为?
a=(1,sin^2(x)),b=(2,sin2x),其中x属于(0,派),若|向量a·向量b|=|向量a||向量b|,则tanx的值为?

a=(1,sin^2(x)),b=(2,sin2x),其中x属于(0,派),若|向量a·向量b|=|向量a||向量b|,则tanx的值为?
a.b = (1,sin^2(x)).(2,sin2x)
= 2+sin2x(sinx)^2
|a|^2 = 1+ (sinx)^4
|b|^2 = 4+(sin2x)^2
|a.b|=|a||b|
=> (2+sin2x(sinx)^2)^2 = (1+ (sinx)^4)(4+(sin2x)^2)
4+4sin2x(sinx)^2+ (sin2x)^2.(sinx)^4 = 4+ (sin2x)^2+(sin2x)^2.(sinx)^4 + 4(sinx)^4
(sin2x)^2-4sin2x(sinx)^2+4(sinx)^4 =0
(sin2x-2(sinx)^2)^2 =0
sin2x= 2(sinx)^2
2sinxcox = 2(sinx)^2
sinx(sinx-cosx)=0
sinx = cosx
tanx = 1

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