A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

how do i verify (cos x/ 1 + sin x) + (1 + sin x/ cos x) = 2 sec x? i don't know how to verify anything at all can someone explain how it works?

  • This Question is Closed
  1. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\huge\rm \frac{ \cos(x) }{ 1+\sin(x) } +\frac{ 1+\sin(x) }{ \cos(x) }\] 1)what is the common denominator ?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i dont know

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i really dont know anything about this

  4. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    alright let's change that to `simple` algebra

  5. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\huge\rm \frac{ x }{ y }+\frac{ y }{ x }\] what's the common denominator ?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    xy

  7. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    okay let's say y represent 1+sinx and x = cos(x) \[y=1+\sin(x)\] \[x=\cos(x)\] now can you tell me what would be the common denominator\[\huge\rm \frac{ \cos(x) }{ 1+\sin(x) } +\frac{ 1+\sin(x) }{ \cos(x) }\] for this question :=)

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1+sinx*cosx ?

  9. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    PERFECT!

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hi i speak Arabic

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    salam alakom

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Nnesha

  13. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\huge\rm \frac{ \cos(x) }{ \color{red}{1+\sin(x)} } +\frac{ 1+\sin(x) }{\color{blue}{ \cos(x)} }\] \[\huge\rm \frac{ \cos(\color{blue}{cos}) + (\color{reD}{1+\sin})(1+\sin)}{ \cos(x) (1+\sin(x))}\] multiply the numerator of `1st fraction` by the `denominator` of 2nd fraction multiply the numerator of `2nd fraction` with the denominator of `1st fraction`

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so would it become cos^2x and (1+sin)^2 on the numerator??

  15. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes right!!!

  16. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[(1+\sin(x))^2 = (1+\sin)(1+\sin)\] (1+sin)^2 is same as (1+sin)(1+sin) foil it

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and what happens when i foil it?

  18. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you will get 3 terms :3

  19. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    then you will be able to cancel out some stuff at the numerator :=)

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 1+2sinx+sin^2x ???

  21. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes right \[\huge\rm \frac{ \color{ReD}{cos^2x}+1+2sinx+\sin^2x }{ cosx(1+sinx) }\] cos^2x= what ? familiar with the identity ?

  22. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\huge\rm sin^2 \theta+\cos^2\theta=1\] this one solve for cos^2

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cos^2=1-sin^2 ?

  24. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    replace cos^2 with 1-sin^2 and then simplify !

  25. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\huge\rm \frac{ \color{ReD}{1-sin^2x}+1+2sinx+\sin^2x }{ cosx(1+sinx) }\]

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2+2sinx ?

  27. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes! what is common factor ?

  28. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\huge\rm \frac{ 2+2sinx }{ \cos(x)(1+sinx) }\] 2+sinx what is common in both terms?

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sinx?

  30. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    no first term is 2 and 2nd one is 2sinx so sinx isn't common

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 2

  32. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes right take out the 2 what will you get ?

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sinx

  34. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    nah

  35. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    when you take out 2 from 2 what will you have left wth?

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0

  37. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    haha well no in other words you have to divide both terms with the common factor so \[\huge\rm \frac{ 2}{ 2} +\frac{ 2sinx }{ 2 } =2(??+???)\]

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1+sinx ?

  39. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes! and we should keep the common factor outside the parentheses \[\huge\rm \frac{ 2(1+sinx) }{ cosx(1+sinx) }\]

  40. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    simplify! that

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2/cosx

  42. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yes right and last step ?

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i dont know

  44. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    thats fine! 2/cosx is same as \[\huge\rm 2 \times \frac{ 1 }{ cosx }\]

  45. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    and 1/cosx= ??

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    secx

  47. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so 2/cosx= ? :=)

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    EXCITING

  49. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i honestly have no idea how to do anything with identities so thank you

  50. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ikr! trig is FUN(well i hate graph)

  51. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    my pleasure! :=) welcome to openstudy!

  52. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \(\color{blue}{\text{Originally Posted by}}\) @rami2021 salam alakom \(\color{blue}{\text{End of Quote}}\) Walikum salam and yeah arabic is my fvt language but all i know is *kafya halik ?? ;~;

  53. Nnesha
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sorry about that alejand :3

  54. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no problem!

  55. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i'm about to post another question, i have one left

  56. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.