已知a、b满足(1-cos2a)/(sinacosa)=1,tan(a-b)=-2/3
1.求tana的值
因为cos2a=1-2sin²a
由题知,(1-cos2a)/(sinacosa)=1
所以,2sin²a / (sinacosa)=1
所以,
sina / cosa = 1/2
即
tana=1/2
2.求tan(2a-b)的值
因为tana=1/2,tan(a-b)=-2/3
所以,
tan(2a-b)
=[tana+tan(a-b)] / [1-tana*tan(a-b)]
=[(1/2)+(-2/3)] / [1-(1/2)(-2/3)]
= -1/8