Trigonometry

how do i evaluate this?

1+tan 200(degrees) tan 80(degrees)/tan200(degrees)-tan 80(degrees)

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  1. Recall the sum of angles for tan:

    tan(A-B) = (tanA-tanB)/(1+tanAtanB)

    You have the reciprocal of that, so what you have is

    cot(200-80) = cot(120) = -1/√3

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  2. I am sure you meant:
    (1+tan 200° tan 80°)/ (tan200°-tan 80°)
    --- those brackets are critical

    recall:
    tan(A-B)
    = (tanA - TanB)/( 1 + tanAtanB)
    = 1/[ (1+tanAtanB)/(tanA - tanB) ]

    tan(200-80) = tan 120 = - tan60° = -√3
    = (tan 200 - tan80)/(1 + tan200tan80)
    = -1/√3

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