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Math Help - Trig Equation

  1. #1
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    Red face Trig Equation

    This is a question taken from my grade 12 math textbook. I'm really not sure how to solve this problem, so any help is really appreciated!

    Determine solutions for tanxcos^2x - tanx = 0 in the interval x Є [-2p, 2p]


    The answer taken from the textbook is: -2p,-p, 0, p, 2p

    Thanks in advance!
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  2. #2
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    \tan x \cos 2x - \tan x = 0

    \tan x \cos 2x = \tan x

    divide both sides by tan?

    \cos 2x  = 1

    Can you finish it?
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  3. #3
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    \displaystyle \tan{x}\cos^2{x} - \tan{x} = 0

    \displaystyle \tan{x}(\cos^2{x} - 1) = 0

    \displaystyle \tan{x} = 0 or \displaystyle \cos^2{x} - 1 = 0

    \displaystyle \tan{x} = 0 or \displaystyle \cos{x} = \pm 1

    \displaystyle x = n\pi where \displaystyle n \in \mathbf{Z} or \displaystyle x = m\pi where \displaystyle m \in \mathbf{Z}.


    Therefore in the period \displaystyle [-2\pi, 2\pi] the solutions are \displaystyle \left\{-2\pi, -\pi, 0, \pi, 2\pi\right\}.


    BTW Pickslides, \displaystyle \tan{x} could be \displaystyle 0, so you really shouldn't divide both sides by it...
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  4. #4
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    Ahh, okay. Thank you!
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