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

题目

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

答案

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
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