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Trig function help

  1. Aug 8, 2016 #1
    1. The problem statement, all variables and given/known data
    Let C=cosx. Write sec(2x)csc(x)sin(2x) as a function of C.

    3. The attempt at a solution

    Am I on the right track

    1/cos(2x) * 1/sin(x) * 2sin(x)cos(x)

    1/(cos^2(x)-sin^2(x)) * `1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x)

    What would i do from here?
     
  2. jcsd
  3. Aug 8, 2016 #2

    andrewkirk

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    There is one ##\sin x## left in your formula that you need to convert to only using ##\cos x##.
    Having done that, you only need to replace every ##\cos x## by ##C##, then simplify as much as possible.
     
  4. Aug 9, 2016 #3

    ehild

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    So you got ##\frac{1}{\cos^2(x)-\sin^2(x)}\frac{1}{\sin(x)}2\sin(x)\cos(x)=\frac{2sin(x)\cos(x)}{(\cos^2(x)-\sin^2(x))\sin(x)}##

    Why don't you simplify with sin(x)???
     
  5. Aug 9, 2016 #4
    1/(cos^2(x)-sin^2(x)) * `1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x)

    1/(cos^2(x)-(1-cos^2(x) * 1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x)

    simplifying this I get

    1/(cos(x)-1)

    =1/(C-1)

    Is this the correct answer?
     
  6. Aug 9, 2016 #5
    made a mistake it should be

    2C/(2C^2-1)
     
  7. Aug 9, 2016 #6

    ehild

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    Finally, that is correct.
     
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