数学题4sin10sin50sin70求值？

来源：百度知道 编辑：UC知道 时间：2024/06/19 12:12:09
哪位大哥大姐帮我解决了吧！谢谢了！

答案为；1/2,
4sin10sin50sin70
=4cos80cos40cos20
=4cos80cos40cos20sin20/sin20
=2cos80cos40sin40/sin20
=sin80cos80/sin20
=2sin80cos80/2sin20
=sin160/2sin20
=1/2
其实不止这一种方法，还有很多种，记得给我加分啊，谢谢啊1

0.5

0.5保证正确，楼主多给点分，谢谢！

4sin10sin50sin70
=4cos80cos40cos20
=4cos80cos40cos20sin20/sin20
=2cos80cos40sin40/sin20
=sin80cos80/sin20
=2sin80cos80/2sin20
=sin160/2sin20
=1/2

4sin10sin50sin70
=2sin50[cos(10-70)-cos(10+70)]
=2sin50[cos60-cos80]
=sin50-2sin50cos80
=sin50-[sin(50+80)+sin(50-80)]
=sin50-sin130+sin30
=sin50-sin50+sin30
=1/2

4sin10sin50sin70
=4cos20cos40cos80
=4cos80(cos(20+40)+cos(40-20))/2
=2cos80(cos60+cos20)
=2cos80cos60+2cos80cos20
=cos(80+60)+cos(80-60)+cos(80+20)+cos(80-20)
=-cos40+cos20-cos80+cos60
=-(cos40+cos80)+cos20+cos60
=-2cos((80+40)/2)cos((80-40)/2)+cos20+cos60
=-2cos60cos20+cos20+cos60
=