化简sin(π/24)sin(11π24)sin(7π/12)

题目

化简sin(π/24)sin(11π24)sin(7π/12)

答案

sin(π/24)sin(11π24)sin(7π/12)
=0.5*(cos(11π24-π/24)-cos(11π/24+π/24))sin(7π/24)
=0.5(cos(5π/12)sin(7π/12))
=0.25(sin(π)+sin(π/6))
=0.25*0.5
0.125