若a属于(0,派/4),B属于(0,派),且tan(a -B)=1/2,tanB=-1/7,则2a -B
问题描述：
若a属于(0,派/4),B属于(0,派),且tan(a -B)=1/2,tanB=-1/7,则2a -B
答
tan(a -B)=1/2，tanB=-1/7
tana=tan(a-b+b)=[tan(a-b)+tanb]/[1-tan(a-b)tanb]=5/14÷15/14=1/3
tan(2a-b)=tan(a-b+a)=[tan(a-b)+tana]/[1-tan(a-b)tana]=5/6÷5/6=1
2a-b=π/4
答
tan2(a-B)=2tan(a-B)/(1-tan²(a-B))=2*(1/2)/(1-1/4)=4/3,tan(2a -B)=tan[2(a-B)+B]=tan2(a-B)tanB/(1-tan2(a+B)tanB)=[4/3+(-1/7)]/[1-(4/3)(-1/7)]=1,由于a属于(0,π/4),2a属于(0,π/2)B属于(0,π),由于tanB...