已知sin(7/12π+α)=2/3,求cos(α-11/12π)的值

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已知sin(7/12π+α)=2/3,求cos(α-11/12π)的值
已知sin(7/12π+α)=2/3,求cos(α-11/12π)的值

已知sin(7/12π+α)=2/3,求cos(α-11/12π)的值
∵sin(7/12π+α)=2/3,
α-11/12π=-3π/2+(7π/12+α)
∴cos(α-11/12π)
=cos[-3π/2+(7π/12+α)]
=cos[-3π/2+2π+(7π/12+α)]
=cos[π/2+(7π/12+α)]
=-sin(7π/12+α)
=-2/3