Question

已知sin(π/6+α)=1/3,则cos(2π/3-2α)的值等于

Answer 1

cos(2π/3-2α)
=cos(2a-2π/3)
=cos(2(a-π/3)
=2cos²(a-π/3)-1。。。。余弦二倍角公式
∵cos(a-π/3)
=cos(α+π/6-π/2)
=sin(π/6+α)
=1/3
∴原式
=2*(1/3)²-1
=2/9-1
=-7/9

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Answer 2

cos(2π/3-2α)=cos[π-(π/3+2α)]=-cos(π/3+2α)
sin(π/3+2α)=2sin(π/6+α)cos(π/6+α)=2/3*2√2/3=4√2/9
cos(π/3+2α)=7/9
cos(2π/3-2α)= - 7/9