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Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)求值
题目详情
Sin(π+π/6)Sin(2π+π/6)Sin(3π+π/6).Sin(2008π+π/6)
求值
求值
▼优质解答
答案和解析
（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/6）×sinπ/6×（－sinπ/6）×sinπ/6×·······×（－sinπ/6）×sinπ/6
=（－sinπ/6）^1004×（sinπ/6）^1004
=(1/2）^2008
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