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sin(20)*sin(40)*sin(60)*sin(80)详?
发表于：2024-10-24 00:00:00浏览：4次
问题描述：sin(20)*sin(40)*sin(60)*sin(80)详?
sin20sin40sin80=sin40*0.5[cos60-cos100](积化和差公式)
=(sin40cos60-sin40cos100)/2
=(sin40+2sin40cos80)/4
=(sin40cos40+2sin40cos40cos80)/4cos40
=(0.5sin80+sin80cos80)/4cos40
=(0.5sin80+0.5sin160)/4cos40
=(sin80+sin20)/8cos40(和差化积)
=2sin50cos30/8cos40
=2cos40cos30/8cos40
=cos30/4
sin20sin40sin60sin80=sin60cos30/4=sin60sin60/4=3/16
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