已知0<a<π/2<b<π,又sina=3/5，cos（a+b=-4/5），则sinb等于多少

答案是24/25
要过程

0<a<π/2<b<π,
π/2<a+b<3π/2
cos(a+b)=-4/5 ,sina=3/5
sin(a+b)=3/5
cosa=4/5

π/2<b<π
所以sinb>0

sinb=sin(a+b-a)
=sin(a+b)cosa-sina*cos(a+b)
=3/5*4/5-3/5*(-4/5)
=12/25+12/25
=24/25

cos(a+b)=cosa*cosb - sina*sinb = -4/5 sin(a+b)=sina*cosb + cosa*sinb = 3/5 sina = 3/5, cosa = 4/5 sinb = 24/25

你题目写错了吧 sina=3/5??

cos(a+b)=cosa*cosb - sina*sinb = -4/5 sin(a+b)=sina*cosb + cosa*sinb = 3/5 sina = 3/5, cosa = 4/5 sinb = 24/25

0<a<π/2<b<π,又sina=3/5

所以cosa=4/5

cos(a+b)=cosacosb-sinasinb=-4/5

cosb4/5-3/5sinb=-4/5

4cosb-3sinb=-4

cosb=(3sinb-4)/4

cos^b=1-sin^2b=(3sinb-4)^2/16

16-16sin^2b=9sin^2b+16-24sinb

24sinb=25sin^2b

sinb不等于0

哪里不清请追问，满意请采纳，谢谢~~

所以sinb=24/25

0<a<π/2<b<π, π/2<a+b<3π/2 cos(a+b)=-4/5 ,sina=3/5 则可求得： sin(a+b)=-3/5或3/5，cosa=4/5 sinb=sin(a+b-a) =sin(a+b)cosa-sina*cos(a+b) =-3/5*4/5-3/5*(-4/5) =0（因为π/2<b<π，故舍去此值） 或 sinb=sin(a+b-a) =sin(a+b)cosa-sina*cos(a+b) =3/5*4/5-3/5*(-4/5) =24/25 所以sinb=24/25