Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)求值

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Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)求值

Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)求值
Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)
求值

Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)求值
(sinπ×cosπ/6+cosπ×sinπ/6)×(sin2π×cosπ/6+cos2π×sinπ/6)······(sin2008π×cosπ/6+cos2008π×sinπ/6)
=(-sinπ/6)×sinπ/6×(-sinπ/6)×sinπ/6×·······×(-sinπ/6)×sinπ/6
=(-sinπ/6)^1004×(sinπ/6)^1004
=(1/2)^2008