已知tan(a-b)=1/2,tanb=-1/7,且a,b∈(0,π),则2a-b=________
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已知tan(a-b)=1/2,tanb=-1/7,且a,b∈(0,π),则2a-b=________
已知tan(a-b)=1/2,tanb=-1/7,且a,b∈(0,π),则2a-b=________
已知tan(a-b)=1/2,tanb=-1/7,且a,b∈(0,π),则2a-b=________
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
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<tana=1/3<1 ,得0 <a< π/4
∵tanb=-1/7 >-1 且0<b<π
∴3π/4 <b<π
-π<(2a-b)<-π/4
所以
2A-B = -3π/4