若锐角a,b满足cosa=4/5,cos(a+b)=3/5,则sinb=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/14 21:29:27
若锐角a,b满足cosa=4/5,cos(a+b)=3/5,则sinb=?
x͊0_eB-T$MdVb_eepƥr%`Gk\ smYY=97$*fn8.~9Ln▧Ƴ|`E5H)HG<2pc0İC{8-`z).|*ăv0sFu+@l %ss?P" >Npf2=lbە۬^/AÙ

若锐角a,b满足cosa=4/5,cos(a+b)=3/5,则sinb=?
若锐角a,b满足cosa=4/5,cos(a+b)=3/5,则sinb=?

若锐角a,b满足cosa=4/5,cos(a+b)=3/5,则sinb=?
cosa=4/5,sina=3/5
cos(a+b)=cosacosb-sinasinb
3/5=4/5cosb-3/5sinb
3=4cosb-3sinb
(3+3sinb)^2=16cos^2b=16(1-sin^2b)
9+18sinb+9sin^b=16-16sin^2b
25sin^2b+18sinb-7=0
(25sinb-7)(sinb+1)=0
sinb=7/25 sinb=-1(舍去)

答案不错

一楼正解