(sin10+sin50)/(sin35×sin55)的值详细过程详细为什么sin10+sin50等于cos20?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/27 22:19:58
(sin10+sin50)/(sin35×sin55)的值详细过程详细为什么sin10+sin50等于cos20?(sin10+sin50)/(sin35×sin55)的值详细过程详细为什么sin10

(sin10+sin50)/(sin35×sin55)的值详细过程详细为什么sin10+sin50等于cos20?
(sin10+sin50)/(sin35×sin55)的值详细过程详细
为什么sin10+sin50等于cos20?

(sin10+sin50)/(sin35×sin55)的值详细过程详细为什么sin10+sin50等于cos20?
sin10 + sin50
= sin(30-20) + sin(30+20)
= 2 * sin30 * cos20
= cos20
sin35 * sin55
= sin35 * cos35
= 1/2 * sin70
= 1/2 * cos20
∴ (sin10 + sin50) / (sin35 * sin55)
= cos20 / (1/2 * cos20)
= 2

sin10+sin50=cos20
sin35·sin55= -[cos(35+55)-cos(35-55)]/2= (cos20-cos90)/2= cos20/2
(sin10+sin50)/(sin35×sin55)=2

sin10 + sin50
= sin(30-20) + sin(30+20)
= 2 * sin30 * cos20
= cos20
sin35 * sin55
=sin35*sin(90-35)
=sin35*cos35
= 1/2 * sin70
= 1/2 * cos20
∴原式= cos20 / (1/2 * cos20)
= 2