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March 27, 2017

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cos[(tan^-1(3/4))+(cos^-1(9/41))]

  • Trig - ,

    let tan^-1 (3/4) = A and let cos^-1 (9/41) = B

    then cos[(tan^-1(3/4))+(cos^-1(9/41))]
    = cos(A + B)
    = cosA cosB - sinA sinB

    IF tan^-1 (3/4) = A
    then tanA = 3/4
    ---> sinA = 3/5 and cosA = 4/5, recognize the 3-4-5 right angled triangle

    if cos^-1 (9/41) = B
    then cosB = 9/41
    ---> x^2 + y^2 = r^2
    81 + y^2 = 1681
    y^2 = 1600
    y = √1600 = 40 and thus sinB = 40/41

    so back to
    cosA cosB - sinA sinB
    = (4/5)(9/41) - (3/5)(40/41) = -84/205

    ( I tested my answer with my calculator, it is correct)

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