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关于一到数学三角函数计算题.cos兀/17×cos2兀/17×cos4兀/17×8兀/17=
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关于一到数学三角函数计算题.
cos兀/17×cos2兀/17×cos4兀/17×8兀/17=
cos兀/17×cos2兀/17×cos4兀/17×8兀/17=
▼优质解答
答案和解析
令a=π/17
原式=cosacos2acos4acos8a
=2sinacosacos2acos4acos8a/2sina
=sin2acos2acos4acos8a/2sina
=2sin2acos2acos4acos8a/4sina
=sin4acos4acos8a/4sina
=2sin4acos4acos8a/8sina
=sin8acos8a/8sina
=sin16a/16sina
=sin(16π/17)/16sin(π/17)
=sin(π-π/17)/16sin(π/17)
=sin(π/17)/16sin(π/17)
=1/16
原式=cosacos2acos4acos8a
=2sinacosacos2acos4acos8a/2sina
=sin2acos2acos4acos8a/2sina
=2sin2acos2acos4acos8a/4sina
=sin4acos4acos8a/4sina
=2sin4acos4acos8a/8sina
=sin8acos8a/8sina
=sin16a/16sina
=sin(16π/17)/16sin(π/17)
=sin(π-π/17)/16sin(π/17)
=sin(π/17)/16sin(π/17)
=1/16
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