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Trig

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True or false?

tan x = tan(x-6pi)

  • Trig - ,

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

    RS = tan(x-6π)
    = (tanx - tan 6π)/(1 + tanxtan 6π)

    but 6π is coterminal with 2π (6π is 3 rotations, and 2π is one rotation
    so tan 6π = tan 2π = 0

    = (tanx - 0)/(1+ ) = tanx = LS

    so the statement is true

    or

    tan(-A) = -tanA
    so tan(x-6π) = - tan(6π-x)
    = -tan(2π-x) , since 6π is coterminal with 2π
    = -( -tan(x) ) , by the CAST rule
    = tanx

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