已知sin(a+π/12)=1/3,则cos(a+7π/12)的值等于

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已知sin(a+π/12)=1/3,则cos(a+7π/12)的值等于

cos(a+7π/12)
=cos[(a+π/12)+π/2]
=cos(a+π/12)cos(π/2)-sin(a+π/12)sin(π/2)
=0-1/3*1
=-1/3