(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
(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