Question

tan(a-b)=1/2.tanb=-1/7,且a,b∈（0,π）.求2a-b的值

Answer 1

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