A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Verify the identity. cotangent of x to the second power divided by quantity cosecant of x plus one equals quantity one minus sine of x divided by sine of x

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\cot^2x/\csc x +1 = 1 - \sin x/\sin x\]

  2. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    try changing LHS to sine and cosines

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

    (cos^2(x)/sin^2(x))/1/sin(x) = (cos^2(x)/sin^2(x))/sin(x)

  4. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    just checking is the question |dw:1438357529236:dw|

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

    (cos^2(x)/sin^2(x))/1/sin(x)+sin(x)/sin(x) = (cos^2(x)/sin^2(x))/sin(x)

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

    yes

  7. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok thnx

  8. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i'll write s for cos x and s for sin x |dw:1438357934242:dw| --

  9. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    can you continue? 2 more steps and you are home

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

    almost let me look at it

  11. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (1 - s) will cancel out

  12. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry (1 + s) will cancel out

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

    on the third step where did you get c^2/s^2

  14. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    c^2 / s^2 was carried on from second step

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

    so the second step was simplified to that

  16. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    - not very readable I know!

  17. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

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

    ok so 1+s/s simplifies to s^2?

  19. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no in the second step c^2 / s^2 is divided by (1+s) / s so we invert the (1+ s) / s to s/(1 + s) then multiply

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

    I understand now I just had to look at the equation a bit more

  21. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and in 4th step we replace cos^x by 1 - sin^ x

  22. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    cos^2 x by 1 - sin^2 x

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

    ok

  24. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this is the difference of 2 squares so simplifies to (1 - s)(1 + s)

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

    yep i understand that

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

    im ready for the next two steps

  27. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so now we can cancel out (1 + s) which appears in the top and bottom of the fractions |dw:1438358863645:dw|

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

    thanks so much

  29. welshfella
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw

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

    \[\frac{1-\sin(x)}{\sin(x)}=\frac{1}{\sin(x)}-\frac{\sin(x)}{\sin(x)}=\csc(x)-1\] \[\implies (\csc(x)-1).\frac{(\csc(x)+1)}{(\csc(x)+1)}=\frac{\csc^2(x)-1}{\csc(x)+1}=\frac{\cot^2(x)}{\csc(x)+1}\]

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

    I've made use of the identities \[(a-b)(a+b)=a^2-b^2\] and \[1+\cot^2(x)= \csc^2(x)\]

  32. 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.