已知tan(α-派/12)=2,则tan(α-派/3)的值为?
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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?
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