Question

已知8(cos2a+b)+5cosb=0,求tan(a+b)*tana

急啊

Answer 1

8cos(2a+b)+5cosb=0
8cos(a+b+a)+5cos(a+b-a)=0
8cos(a+b)cosa-8sin(a+b)sina+5cos(a+b)cosa+5sin(a+b)sina=0
13cos(a+b)cosa=3sin(a+b)sina
13/3=[sin(a+b)sina]/[cos(a+b)cosa]
tan(a+b)tana=13/3

Answer 2

8(cos2a+b)+5cosb=8(cosa+b+a)+5cos(a+b-a)
=8cos(a+b)cosa-8sin(a+b)sina+5cos(a+b)cosa+5sin(a+b)sina=0
13cos(a+b)cosa=3sin(a+b)sina tan(a+b)tana=13/3