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Homework Help: Simplify math issue

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    simplify:
    [tex] \sin\theta\sec\theta+\cos\theta\csc\theta[/tex]


    2. Relevant equations
    Reciprocal identities, Quotient identities, Pythagorean identities


    3. The attempt at a solution

    [tex] \sin\theta\sec\theta+\frac{1}{\sec\theta}\frac{1}{\sin\theta}[/tex]

    [tex] \sin\theta\sec\theta+\frac{1}{\sin\theta\sec\theta}[/tex]

    and this is where i get stuck...can i get help from anyone?
     
  2. jcsd
  3. Feb 21, 2010 #2

    tiny-tim

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    Hi PanTh3R! :smile:

    (have a theta: θ :wink:)

    You need to be systematic …

    keep all the sin and cos, get rid of the sec and csc. :wink:

    Try again. :smile:
     
  4. Feb 21, 2010 #3
    Re: simplify

    so i get....

    [tex]\sin\theta\frac{1}{\cos\theta}+cos\theta\frac{1}{\sin\theta}[/tex]

    then i put each in one fraction right?

    [tex]\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}[/tex]

    to

    [tex]\tan\theta+cot\theta[/tex]

    is that the simplest it can get?
     
  5. Feb 21, 2010 #4

    tiny-tim

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    Hi PanTh3R! :wink:

    This is elementary algebra …

    put both fractions over the same denominator (the LCM). :smile:
     
  6. Feb 21, 2010 #5
    Re: simplify

    im sorry im really bad with these i just started doing them um so i do

    [tex]\frac{\sin^2\theta+\cos\theta}{\cos\theta\sin\theta}[/tex]

    i still don't get it wont that make it more complicated? :confused:
     
  7. Feb 21, 2010 #6

    tiny-tim

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    Bottom right, top wrong. :wink:
     
  8. Feb 21, 2010 #7
    Re: simplify

    would it be....

    [tex]\frac{\sin^2\theta+\cos^2\theta}{\cos\theta\sin\theta}[/tex]

    then

    [tex]\frac{1-\cos^2+\cos^2\theta}{\cos\theta\sin\theta}[/tex]

    into

    [tex]\frac{1}{\cos\theta\sin\theta}[/tex]

    i feel so frustrated :confused: sry
     
  9. Feb 21, 2010 #8
    Re: simplify

    Looks like that's the simplest you can get it.
     
  10. Feb 22, 2010 #9
    Re: simplify

    [tex]2cosec(2\theta)[/tex] would seems better.
     
  11. Feb 22, 2010 #10

    Mentallic

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    Re: simplify

    It depends if the OP has been exposed to double-angles yet. Trigonometric simplifications of this form are commonly taught before the student ever learns that [itex]2sin\theta cos\theta=sin(2\theta)[/itex]
     
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