证明:tan(α+π/4)+tan(α+3π/4)=2tan2α
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证明:tan(α+π/4)+tan(α+3π/4)=2tan2α
tan(α+π/4)+tan(α+3π/4)
=(tanα+tanπ/4)/(1-tanαtanπ/4)+(tanα+tan3π/4)/(1-tanα+tan3π/4)
=(tanα+1)/(1-tanα)+(tanα-1)/(1+tanα)
={(tanα+1)*(1+tanα)+(tanα-1)*(1-tanα)}/{(1+tanα)*(1-tanα)}
=(4tanα)/(1-tan^2α)
=2tan2α
=(tanα+tanπ/4)/(1-tanαtanπ/4)+(tanα+tan3π/4)/(1-tanα+tan3π/4)
=(tanα+1)/(1-tanα)+(tanα-1)/(1+tanα)
={(tanα+1)*(1+tanα)+(tanα-1)*(1-tanα)}/{(1+tanα)*(1-tanα)}
=(4tanα)/(1-tan^2α)
=2tan2α
证明:tan(α+π/4)+tan(α+3π/4)=2tan2α
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