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Simplifying this trig solution

  1. Jan 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Simplify this expression: csc(x)sqrt(sec^2(x)-1) with 0 less than or equal x less than pi/2.


    2. Relevant equations



    3. The attempt at a solution
    Not really sure what they want here, but would a good place to start be to square the entire expression to get rid of the square root or would that make things more complicated? and what is meant by x being between 0 and pi/2?
     
  2. jcsd
  3. Jan 12, 2012 #2

    SammyS

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    Squaring the expression is not recommended.

    Do you know a trig identity relating tan2(x) and sec2(x) ?

    Use that.
     
  4. Jan 12, 2012 #3
    gotcha, the Pythagorean identity 1+tan^2(x)=sec^2(x)
     
  5. Jan 12, 2012 #4
    ok, I think I got this if anyone wants to confirm, still not sure about the x greater or equal to 0 and less than or equal to pi/2, but here goes. csc(x)sqrt(sec^2(x)-1) turns into csc(x)sqrt(tan^2(x)+1-1) after the Pythagorean identity, then simplifies to csc(x)tan(x) after you do the square root. csc(x)tan(x) is equal to 1/sin(x) * 1/cos(x), those multiply together to give 1/cos(x) and that equals sec(x), that sound right?
     
  6. Jan 12, 2012 #5
    I think you mean [itex]\frac{1}{sinx}\times\frac{sinx}{cosx}[/itex].

    But yes, that looks right.
     
  7. Jan 12, 2012 #6

    SammyS

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    The restriction: 0 ≤ x < π/2 means that all of the trig functions give a non-negative result and in particular, [itex]\sqrt{\tan^2(x)=\tan(x)}[/itex] without the ± sign.
     
  8. Jan 12, 2012 #7
    yes, bread18, i did mean [tex]\frac{sinx}{\cos(x)}[/tex]

    Thanks by the way!
     
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