tan(a-π/12) =2,tan(a-π/3)的值
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tan(A+B) = (tanA+tanB)/(1-tanAtanB),把(a-π/3)看做整体,tan(π/4)=1
tan(a-π/12)=tan(a-π/3+π/4)=[tan(a-π/3)+tan(π/4)]/[1-tan(a-π/3)×tan(π/4)]
=[tan(a-π/3)+1]/[1-tan(a-π/3)]=2
tan(a-π/3)+1=[1-tan(a-π/3)]×2
再把tan(a-π/3)看做整体,3tan(a-π/3）=1
∴tan(a-π/3)=1/3
tan(a-π/12)=tan(a-π/3+π/4)=[tan(a-π/3)+tan(π/4)]/[1-tan(a-π/3)×tan(π/4)]
=[tan(a-π/3)+1]/[1-tan(a-π/3)]=2
tan(a-π/3)+1=[1-tan(a-π/3)]×2
再把tan(a-π/3)看做整体,3tan(a-π/3）=1
∴tan(a-π/3)=1/3
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