sin（π+π/6）sin（2π+π/6）sin（3π+π/6）.sin（2010π+π/6）
问题描述：
sin（π+π/6）sin（2π+π/6）sin（3π+π/6）.sin（2010π+π/6）
答
sin（π+π/6）sin（2π+π/6）sin（3π+π/6）......sin（2010π+π/6）
=(-1/2)(1/2)(-1/2)(1/2)......(-1/2)(1/2)
=-1/2^2010
答
sin（π+π/6）= -sinπ/6 = -1/2；
sin（2π+π/6）=sinπ/6= 1/2；.
所以原式等价于 = (-1/2)(1/2)(-1/2).(1/2)
含负号的项共有 2010/2=1005个,是奇数,故原式= -(1/2)^2010.