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Question

If tanα=m/(m+1),tanβ=1/(2m+1), show that α+β=π/4

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Solution

tan(α+β)=tanα+tanβ1tanαtanβ={m/(m+1)}+{1/(2m+1)}1{m/(m+1)}+{1/(2m+1)}=2m2+2m+1m2+3m+1m=1α+β=π4

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