Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

SugarRainbow

  • 2 years ago

HELP SIMPLIFY (sinx/1-cosx)+(1-cosx/sinx)

  • This Question is Closed
  1. Shadowys
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I believe you have attempted to do it. Where were you stuck? Though the answer isn't that pretty..

  2. SugarRainbow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay so i was thinking of multiplying cosx to the numerator and denominator of the (sinx/1-cosx) so then the denominator will be sin^2x and then multiply sinx to (1-cosx/sinx) so that both denominators will bbe sin^2x is that even a good first step to take?

  3. seitys
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sinx/(1-cosx)*(1+cosx)/(1+cosx) + (1-cosx/sinx) =sinx(1+cosx)/sin^2 x + (1-cosx/sinx) =(1+cosx/sinx)+(1-cosx/sinx) =(1+cosx+1-cosx)/sinx =2/sinx

  4. SugarRainbow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why did you do this sinx(1+cosx)/sin^2 x or how'd that happen

  5. SugarRainbow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh wait nevermind i see what you did there

  6. seitys
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when you multiply (1-cosx) by its conjugate (1+cosx), you get (1-cos^2 x) which is just sin^2 x --> sin^2 x + cos^2 x = 1 so 1-cos^2 x=sin^2 x

  7. SugarRainbow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay well how did that turn into (1+cosx/sinx)?

  8. seitys
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    there is a sinx in the numerator and a sin^2 x in the denominator. so 1 of them cancels out.

  9. SugarRainbow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and you got 2/sinx because the +cosx and the -cosx cancel out right?

  10. seitys
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    because that is the remaining denominator for both terms.

  11. seitys
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  12. seitys
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you can simplify it even further because 1/sinx = cscx so it can also be written as 2cscx

  13. SugarRainbow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh okay thank you this was really helpful

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.