已知函数f(x)=2cos(x-π/6)sin(x+π/6)-√3*(sin(x-π/6))^2+sin(x-π/6)c
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已知函数f(x)=2cos(x-π/6)sin(x+π/6)-√3*(sin(x-π/6))^2+sin(x-π/6)cos(x-π/6),π表示圆周率.
(Ⅰ)试求f(x)的最小正周期T.
(Ⅱ)已知对任意的x∈【0,π/2】,不等式√2/2*(2a+3)*f(x/2+π/8)+(6√2)/f(x/2+π/8)-f(x)<3a+6恒成立,求实数a的取值范围.
(Ⅰ)试求f(x)的最小正周期T.
(Ⅱ)已知对任意的x∈【0,π/2】,不等式√2/2*(2a+3)*f(x/2+π/8)+(6√2)/f(x/2+π/8)-f(x)<3a+6恒成立,求实数a的取值范围.
f(x)=2cos(x-π/6)sin(x+π/6)-√3*(sin(x-π/6))^2+sin(x-π/6)cos(x-π/6)
=sin2x+sin(π/3)-(√3/2)[1-cos(2x-π/3)]+(1/2)sin(2x-π/3)
=sin2x+(√3/2)cos(2x-π/3)+(1/2)sin(2x-π/3)
=2sin2x,
(Ⅰ)f(x)的最小正周期T=π.
(II)f(x/2+π/8)=2sin(x+π/4)=√2(sinx+cosx),
设u=sinx+cosx,x∈[0,π/2],则1
再问: 答案是a>3,是否有算错的地方?请您再仔细看看好吗?急用
再答: 我复查一遍,未发现错误。请您检查一下。如有错误,告诉我。
=sin2x+sin(π/3)-(√3/2)[1-cos(2x-π/3)]+(1/2)sin(2x-π/3)
=sin2x+(√3/2)cos(2x-π/3)+(1/2)sin(2x-π/3)
=2sin2x,
(Ⅰ)f(x)的最小正周期T=π.
(II)f(x/2+π/8)=2sin(x+π/4)=√2(sinx+cosx),
设u=sinx+cosx,x∈[0,π/2],则1
再问: 答案是a>3,是否有算错的地方?请您再仔细看看好吗?急用
再答: 我复查一遍,未发现错误。请您检查一下。如有错误,告诉我。
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