已知tan(a+β)=1/4,tan(β-π/6)=1/3,则tan(a+π/6)=A.1/12B.1/13C.-1/12D.-1/13求分析啊.....

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已知tan(a+β)=1/4,tan(β-π/6)=1/3,则tan(a+π/6)=A.1/12B.1/13C.-1/12D.-1/13求分析啊.....

已知tan(a+β)=1/4,tan(β-π/6)=1/3,则tan(a+π/6)=A.1/12B.1/13C.-1/12D.-1/13求分析啊.....
已知tan(a+β)=1/4,tan(β-π/6)=1/3,则tan(a+π/6)=
A.1/12
B.1/13
C.-1/12
D.-1/13
求分析啊.....

已知tan(a+β)=1/4,tan(β-π/6)=1/3,则tan(a+π/6)=A.1/12B.1/13C.-1/12D.-1/13求分析啊.....

tan(a+π/6)
=tan[(a+b)-(b-π/6)]
=[tan(a+b)-tan(b-π/6)]/[1+tan(a+b)tan(b-π/6)]
=(1/4-1/3)/(1+1/4×1/3)
=(-1/12)/(13/12)
=-1/12×(12/13)
=-1/13
选D