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Trig Equations With Undefined Values

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data

    1. Simplify:
    [sin(x-pi) / cos(pi - x)] - [tan(x-3pi/2) / -tan(pi + x)

    2. Solve:
    1 - tan(2x + pi/2) = 0, 0 ≤ x ≤ 2pi


    2. Relevant equations

    cos(x - y) = cosxcosy + sinxsiny

    sin(x - y) = sinxcosy + cosxsiny

    tan(x + y) = tanx + tany / 1-tanxtany

    tan (x - y) = tanx - tany / 1 +tanxtany

    3. The attempt at a solution

    For 1. I managed to expand everything according to the compound angle formulas listed above. Then I used the unit circle to come up with some values, which left me with:

    [-cosx / -cosx] - [tanx-tan(3pi/2) / 1 + tanxtan(3pi/2)]
    alskdjaslkdjalskdjalskdjalskdj -[(0 + tanx) / 1-(0)tanx]

    The problem is that I don't know what to do with tan(3pi/2) because it's undefined...
    The same problem persists for 2. I expanded but I don't know what to do with the undefined values. Please help!

    Thank you in advance!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 28, 2012 #2

    LCKurtz

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    Your problem is that the formula $$\tan(a-b)=\frac{\tan a -\tan b}{1 + \tan a \tan b}$$doesn't work for ##a## or ##b## is an odd multiple of ##\pi/2##. Try writing$$
    \tan(a-b) = \frac{\sin(a-b)}{\cos(a-b)}$$and use the addition formulas on that. That will work even when ##\pi/2## is involved.
     
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