tan(a-b)=1/2.tanb=-1/7,且a,b∈（π/2,3π/2）.求2a-b的值

tan(a-b)=1/2.tanb=-1/7,且a,b∈（π/2,3π/2）.求2a-b的值
tan(a-b)=1/2.tanb=-1/7,且a,b∈（π/2,3π/2）.求2a-b的值

tan(a-b)=1/2.tanb=-1/7,且a,b∈（π/2,3π/2）.求2a-b的值
tana=tan(a-b+b)=[tan(a-b)+tanb]/[1-tan(a-b)*tanb]
=(1/2-1/7)/(1+1/2*1/7)
=1/3
所以tan(2a-b)=tan(a+a-b)
=[tana+tan(a-b)]/[1-tana*tan(a-b)]
=(1/3+1/2)/(1-1/3*1/2)
=1
0所以3π/4-π<-b<-3π/4
0-π0所以03π/4所以3π/4因为0所以3π/4所以3π/2<2a<2π或0<2a<π/2
-π<-b<-3π/4
所以π/2<2a-b<5π/4或-π<2a-b<-π/4
tan(2a-b)=1
所以2a-b=-3π/4