Question

sin10°sin30°sin50°sin70°怎么化简

Answer 1

方法1.
原式=sin10*1/2*cos40*cos20
=1/2*2sin10cos10cos20cos40/(2cos10)
=1/2*sin20cos20cos40/(2cos10)
=1/2*sin40cos40/(4cos10)
=1/2*sin80/(8cos10)
=1/2*cos10/(8cos10)
=1/16
方法2.
sin10°sin30°sin50°sin70°
=cos20cos40cos60cos80
=sin20cos20cos40cos60cos80/sin20
=1/2*sin40cos40cos60cos80/sin20
=1/16sin160/sin20
=1/16
方法3.
sin10*sin30*sin50*sin70
=cos10*sin10*sin30*sin50*sin70/cos10
=1/2*sin20*sin70*sin30*sin50/cos10
=1/2*sin20*cos20*sin30*sin50/cos10
=1/4sin40*sin50*sin30/cos10
=1/4sin40*cos40*sin30/cos10
=1/8sin80*sin30/cos10
=1/8cos10*sin30/cos10
=1/8sin30
=1/16

Answer 2

原式=sin10*1/2*cos40*cos20
=1/2*2sin10cos10cos20cos40/(2cos10)
=1/2*sin20cos20cos40/(2cos10)
=1/2*sin40cos40/(4cos10)
=1/2*sin80/(8cos10)
=1/2*cos10/(8cos10)
=1/16