Question

一道高一数学题

计算:cos(pai/15)×cos(2pai/15)×cos(4pai/15)×cos(8pai/15)=?加分呐！谢谢！

Answer 1

原式=[sin(π/15)*cos(π/15)cos(2π/15)cos(4π/15)cos(8π/15)]/sin(π/15)
=[1/2*sin(2π/15)*cos(2π/15)cos(4π/15)cos(8π/15)]/sin(π/15)
={1/2*[1/2*sin(4π/15)cos(4π/15)cos(8π/15)]}/sin(π/15)
={1/4*[1/2*sin(8π/15)cos(8π/15)]}/sin(π/15)
={1/8*[1/2*sin(16π/15)]}/sin(π/15)
=1/16*[-sin(π/15)/sin(π/15)]
=-1/16

Answer 2

sin12×cos12×cos24×cos48×cos96/sin12
=1/2sin24×cos24×cos48×cos96/sin12
=1/4sin48×cos48×cos96/sin12
=1/8sin96×cos96/sin12
=1/16sin192/sin12
=-1/16sin12/sin12
=-1/16