cos1/9π*cos2/9π*cos3/9π*cos4/9π=?怎么算?答案是1/16,

cos1/9π*cos2/9π*cos3/9π*cos4/9π=?怎么算?答案是1/16,
cos1/9π*cos2/9π*cos3/9π*cos4/9π=?怎么算?答案是1/16,

cos1/9π*cos2/9π*cos3/9π*cos4/9π=?怎么算?答案是1/16,
上下乘16sinπ/9sin2π/9sin3π/9sin4π/9
原式=(2sinπ/9cosπ/9)(2sin2π/9cos2π/9)(2sin3π/9cos3π/9)(2sin4π/9cos4π/9)/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=sin2π/9sin4π/9sin6π/9sin8π/9/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=sin2π/9sin4π/9sin(π-3π/9)sin(π-π/9)/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=sin2π/9sin4π/9sin3π/9sinπ/9/(1616sinπ/9sin2π/9sin3π/9sin4π/9)
=1/16

cos1/9π*cos2/9π*cos3/9π*cos4/9π
=2sin1/9π*cos1/9π*cos2/9π*cos3/9π*cos4/9π/2sin1/9π
=sin2/9π*cos2/9π*cos3/9π*cos4/9π/2sin1/9π
=sin4/9π**cos3/9π*cos4/9π/4sin1/9π
=sin8/9π**cos3/9π/8sin1/9π
=cos3/9π/8
=cos1/3π/8=1/16

cos1/9π*cos2/9π*cos3/9π*cos4/9π
=8sin1/9π*cos1/9π*cos2/9π*cos3/9π*cos4/9π/8sin1/9π
=sin8/9π*cos3/9π/8sin1/9π
=-1/16