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Trig Identities

  1. Apr 26, 2016 #1
    1. The problem statement, all variables and given/known data

    cot2x + sec2x = tan2x + csc2x

    2. Relevant equations


    3. The attempt at a solution
    I began by working on my left side.

    I got up until
    =cos^4x + sin^2x / sin^2x cos^2x

    And unsure of where to go next.
     
  2. jcsd
  3. Apr 26, 2016 #2

    SteamKing

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    You made a good start working on the LHS. Do the same to the RHS and see what you get.
     
  4. Apr 26, 2016 #3
    On right side I got sin^4x + cos^2x / cos^2x sin^2x , I can't seem to get it
     
  5. Apr 26, 2016 #4

    SteamKing

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    Compare the LHS to the RHS now. Do you notice anything in common?
     
  6. Apr 26, 2016 #5
    L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2x
    = cos^2x / sin^2x + 1 / cos^2x
    = cos^2x + sin^2x / sin^2x cos^2x
    = 1 / sin^2x cos^2x

    R.S = sin^4x / sin^2x cos^2x + cos^2x / sin^2x cos^2x
    = sin^2x / cos^2x + 1 / sin^2x
    = sin^2x + cos^2x / sin^2x cos^2x
    = 1 / sin^2x cos^2x
    Would this be the answer?
     
  7. Apr 26, 2016 #6

    SteamKing

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    I'm having a problem seeing how you go from the expression above to the one below:
    I see that you found the common denominator, but your numerator is incorrect.
    Same comments from the LHS calculations apply above.

    Compare the expression you found on the RHS here with the one you obtained in Post #3:

     
  8. Apr 27, 2016 #7

    SammyS

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    When writing "fractions" with an "in-line" format, one using the " / " character, you need to use parentheses to include (the entire numerator) / (the entire denominator).

    I have added parentheses to what I assume are the proper locations in the above included quote. (Also added a few other items.)
     
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