已知tan（α-派/12）=2,则tan（α-派/3）的值为?

已知tan（α-派/12）=2,则tan（α-派/3）的值为?

解
tan(a-π/12)
=tan[a-(π/3-π/4)]
=tan[(a-π/3)+π/4]
=[tan(a-π/3)+tanπ/4]/[1-tan(a-π/3)tanπ/4]
=2
即
tan(a-π/3)+1=2[1-tan(a-π/3)]
即
tan(a-π/3)+1=2-2tan(a-π/3)
即tan(a-π/3)=1/3