数学题4sin10sin50sin70求值？

答案:6 悬赏:10 手机版

解决时间 2021-04-27 10:04

提问者网友：孤山下
2021-04-26 19:05

最佳答案

五星知识达人网友：冷風如刀
2021-04-26 20:34

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

全部回答

1楼网友：话散在刀尖上
2021-04-27 00:53

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
=-cos20+cos20+cos60
=cos60
=0.5

2楼网友：骨子里都是戏
2021-04-27 00:41

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

3楼网友：迷人又混蛋
2021-04-26 23:47

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

4楼网友：旧脸谱
2021-04-26 23:21

0.5保证正确，楼主多给点分，谢谢！

5楼网友：掌灯师
2021-04-26 21:48

0.5

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