求sin10°x sin50°x sin70°的值

=sin10*cos(90-50)*cos(90-70)
=sin10cos20cos40
=2sin10cos10cos20cos40/2cos10
=sin20cos20cos40/2cos10
=2sin20cos20cos40/4cos10
=sin40cos40/4cos10
=2sin40cos40/8sin(90-10)
=sin80/8sin80
=1/8

和积互化公式
sin70^sin50^sin10=-1/2(cos120-cos20)*sin10=1/2(sin10cos20+1/2sin10)=1/2[1/2(sin30-sin10)+1/2sin10]=1/4*sin3==1/8

或者有个三倍角公式直接可以算出来
sin3x=4sinx*sin(60+x)*sin(60-x)

原式=sin10*cos20*cos40
=sin10*cos10*cos20*cos40/cos10
=0.5*sin20*cos20*cos40/cos10
=0.25*sin40*cos40/cos10
=0.125*sin80/sin80
=0.125

=sin10*cos(90-50)*cos(90-70)
=sin10cos20cos40
=2sin10cos10cos20cos40/2cos10
=sin20cos20cos40/2cos10
=2sin20cos20cos40/4cos10
=sin40cos40/4cos10
=2sin40cos40/8sin(90-10)
=sin80/8sin80
=1/8
sin70^sin50^sin10=-1/2(cos120-cos20)*sin10=1/2(sin10cos20+1/2sin10)=1/2[1/2(sin30-sin10)+1/2sin10]=1/4*sin3==1/8