Question

sin20°sin40°sin60°sin80°的值为

答案为3/16
求过程

Answer 1

需要用的积化和耐茄差公式
2sinasinb=cos(a-b)-cos(a+b)
2sinacosb=sin(a+b)+sin(a-b)
上述公式很容易薯让用和差公式推导

sin20°sin40°sin60°sin80°
=[cos(20°-40°)-cos(20°+40°)]sin80°sin60°/2
=(cos20°sin80°-cos60°sin80°)sin60°/2
={[sin(20°+80°)+sin(80°-20°)]/2-sin80°/2}sin60°/2
={[sin100°+sin60°]/2-sin80°/2}sin60°/2
={sin80°/昌手察2+sin60°/2-sin80/2}sin60°/2
=sin60°/2*sin60°/2
=3/16