求Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)的值

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求Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)的值
求Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)的值

求Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)的值
Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6)...Sin(2008π+π/6)=Sin(π+π/6)Sin(π/6)Sin(π+π/6)...Sin(π/6)=[Sin(π+π/6)]^1004 * [Sin(π/6)]^1004
=[-Sin(π/6)]^1004* [Sin(π/6)]^1004
=[Sin(π/6)]^2004
=(1/2)^2008

由于Sin(π+π/6)=Sin(3π+π/6)=......=Sin(2007π+π/6)
Sin(2π+π/6)=Sin(4π+π/6)=......=Sin(2008π+π/6)
原式=[Sin(π+π/6)Sin(2π+π/6)]的1004次方
=-1/4的1004次方
=1/4的1004次方