若sin(α-π/6)=1/3 则cos(2α-π/3)的值等于

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若sin(α-π/6)=1/3 则cos(2α-π/3)的值等于
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若sin(α-π/6)=1/3 则cos(2α-π/3)的值等于
若sin(α-π/6)=1/3 则cos(2α-π/3)的值等于

若sin(α-π/6)=1/3 则cos(2α-π/3)的值等于
若sin(α-π/6)=1/3
则cos(2α-π/3)
=cos2(α-π/6)
=1-2sin²(α-π/6)
=1-2×(1/3)²
=1-2/9
=7/9

cos(2α-π/3)
= cos【2(α-π/6)】
= 1 - 2sin²(α-π/6)
= 1 - 2×(1/3)²
= 7/9

主要考查诱导公式,变角,二倍角公式
sin(α-π/6)=1/3,
而sin(α-π/6)=cos[π/2-(α-π/6)]
= cos((2π/3)-α),
∴cos((2π/3)-α)=1/3。
所以cos((2π/3)+2α)= cos[2((π/3)+α)]
= 2cos²((π/3)+α)-1
=7/9.

cos[2α-(π/3)]=cos[2(α-π/6)]=1-2sin²[α-(π/6)]
=1-2*(1/3)²
=1-(2/9)
=7/9
——倍角公式:cos2α=1-2sin²α=2cos²α-1