Question

sin10sin30sin50sin70的值= (是度）

是度）
答案是1/16 我要过程

Answer 1

sin10sin30sin50sin70
=(2sin10cos10/2cos10)sin30cos40cos20
=(sin20/2cos10)sin30cos40cos20
=[(1/2sin40)/2cos10]sin30cos40
=[(1/4sin80)/2cos10]sin30
=[(1/4sin80)/2sin80]sin30
=1/8sin30
=1/16

Answer 2

sin10sin30sin50sin70
=sin30（sin10sin50sin70）
=sin30（sin（60-10）sin10sin（60+10））
=sin30*（1/4sin30）
=1/16
三倍角公式

Answer 3

sin10sin30sin50sin70
=sin10cos10sin30sin50sin70/cos10
=sin20sin30sin50sin70/2cos10
=sin40sin30sin50/4cos10
=cos10/16cos10
=1/16

Answer 4

sin10sin30sin50sin70
=1/2*sin10*sin50*sin70
=1/2*sin10*cos20*cos40
=1/2*cos10*sin10*cos20*cos40/cos10
=1/4*sin20*cos20*cos40/cos10
=1/8*sin40*cos40/cos10
=1/16*sin80/cos10
=1/16*cos10/cos10
=1/16