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Prove that 1/tan (1+x)/(1-x)=π/4+1/tanx

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Prove that 1/tan (1+x)/(1-x)=π/4+1/tanx

    • Posted by Anamika Singh 4 years, 4 months ago

    CBSE > Class 12 > Mathematics
    • 1 answers

    Saurabh Singh 4 years, 4 months ago

    LHS = 1/tan(1+x)/(1-x) ( Put x =tany) = tan^-1 (1+x)/(1-x) = tan^-1(1+tany)/(1-tany) = tan^-1 (tanπ/4 + tany)/(1- tanπ/4.tany) = tan^-1[tan(π/4+y)] =π/4 + y = π/4 + tan^-1x (tan^-1 =y) =π/4 + 1/tanx

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