设tanα=1/2,tanβ=1/3,则cot(α+2β)=A.1/2 B.-1/2 C.2 D.-2

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设tanα=1/2,tanβ=1/3,则cot(α+2β)=A.1/2 B.-1/2 C.2 D.-2
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设tanα=1/2,tanβ=1/3,则cot(α+2β)=A.1/2 B.-1/2 C.2 D.-2
设tanα=1/2,tanβ=1/3,则cot(α+2β)=
A.1/2 B.-1/2 C.2 D.-2

设tanα=1/2,tanβ=1/3,则cot(α+2β)=A.1/2 B.-1/2 C.2 D.-2
tan2β=2tanβ/(1-tan²β)=(2×1/3)/(1-1/9)=3/4
故tan(α+2β)=(tanα+tan2β)/(1-tanαtan2β)=(1/2+3/4)/(1-1/2×3/4)=2
所以cot(α+2β)=1/tan(α+2β)=1/2
答案:选A