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maths-trignometry

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Prove that
tan-1 (1/7) + tan-1 (1/13) = tan-1(2/9)

  • maths-trignometry - ,

    let tanA = 1/7 and tanB = 1/13

    then tan(A+B) = (tanA + tanB)/( 1 - tanAtanB)
    = (1/7 + 1/13)/(1 - (1/7)(1/13) )
    = (20/91) / (90/91) = 20/90 = 2/9

    and if we let tanC = 2/9
    then A + B = C

    thus tan^-1 (1/7) + tan^-1 (1/13) = tan^-1 (2/9)

    check with your calculator
    take 2nd Tan (1/7) = 8.13010..
    take 2nd Tan(1/13) = 4.39871
    add them: 12.5288..
    take 2nd Tan(2/9) = 12.5288..

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