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Identities sin, cos, tan etc. stuff

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data

    ((cos x)/(1+sin x))+((1+sin x)/(cos x))

    2. Relevant equations


    2012-03-05_12-13-36_59.jpg


    3. The attempt at a solution

    multiplied the left equation by (cos x)/(cos x) and the right fraction by (1+sin x)/(1+sin x)

    get ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x)

    and I have no idea where to go from here
     
    Last edited by a moderator: Mar 6, 2012
  2. jcsd
  3. Mar 6, 2012 #2

    Mark44

    Staff: Mentor

    What are you trying to do, simplify the expression above?
     
  4. Mar 6, 2012 #3
    Yes, the answer being 2 sec x
     
  5. Mar 6, 2012 #4

    Mark44

    Staff: Mentor

    Expand the numerator and simplify.
    ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x)
     
  6. Mar 6, 2012 #5
    (1-sinx^2) +1 + sinx +1 - sin x

    (1- sinx^2) +2 / (1+sin x)(cos x)

    I don't see how that helps
     
  7. Mar 6, 2012 #6

    Mark44

    Staff: Mentor

    The only thing you did that makes sense is replacing cos2(x) with 1 - sin2(x). I don't get what you did go go from (1 + sin(x))2 to 1 + sin(x) + 1 - sin(x).

     
  8. Mar 6, 2012 #7
    Then what simplifying is there to do?
     
  9. Mar 7, 2012 #8

    Mark44

    Staff: Mentor

    Apparently I wasn't clear. (1 + sin(x))2 ≠ 1 + sin(x) + 1 - sin(x), which seems to be what you're saying.

    The "simplifying" that you need to do is to expand (1 + sin(x))2 to something it is actually equal to.
     
  10. Mar 7, 2012 #9
    Okay it equals (1+sinx)(1-sinx)
    still not way to get to 2secx
     
  11. Mar 7, 2012 #10

    Mark44

    Staff: Mentor

    Because that's wrong, too. (1 + sin(x))2 ≠ (1+sinx)(1-sinx), if that's what you're saying.

    How do you expand (1 + x)2? This is a similar kind of problem.
     
  12. Mar 7, 2012 #11
    Okay it equals (1+sinx)(1+sinx)
    still no way to get to 2secx
     
  13. Mar 7, 2012 #12

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Expand the expression: apply distributivity to work out the brackets.
     
  14. Mar 7, 2012 #13
    All right got it
     
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