A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Ammarah

  • one year ago

Identities HELP FINAL TOMORROW

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

    |dw:1433373713959:dw|

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

    @perl

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

    we should start with the right side?

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

    yess

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

    $$ \Large { \tan x ( 1 + \cos(2x) )= \\ = \tan x ( 1 + 2\cos^2(x)-1 )= } $$

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

    i used the substitution cos(2x) = 2cos^2 x -1

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

    how did u get rid of the cosx>

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

    $$ \Large { \tan x ( 1 + \cos(2x) ) \\ = \tan x ( 1 + \color{red}{ 2\cos^2(x)-1} ) \\= \tan x \cdot 2\cos^2(x) \\= \frac{\sin x}{\cos x } \cdot 2\cos^2(x) \\~\\= 2 \sin x \cos x \\~\\= \color{blue}{\sin(2x)} } $$

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

    the red and blue are substitutions

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

    Trig identities: sin(2x) = 2sin x cos x cos(2x) = 2cos^2 x - 1

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

    i know but u know u cosx was left

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

    how did u get rid of that..

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

    in the last line, 2sin x cos x = sin(2x) , thats a trig identity

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

    You can prove that by use of the addition formula: sin(2x) = sin(x+x) = sin x cos x + cos x sin x = 2 sin x cos x

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

    this is a good resource for identities http://www.purplemath.com/modules/idents.htm

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

    ohkk

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

    i have another queestion

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

    |dw:1433375868645:dw|

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

    Is this the question? $$ \Large \csc x = \frac{\cot ( x/2)}{1 + \cos x } $$

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

    yes

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

    Let's use the half angle identity.

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

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

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

    cot(x/2) = 1 / tan(x/2) = ( 1 + cos x ) / sin x

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

    thats an equivalent identity

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

    cot(x/2) / ( 1 + cos x ) =cot(x/2) * 1 / ( 1 + cos x ) = (1 + cos x ) / sin x * 1 / ( 1 + cos x ) = 1 / sin x = csc x

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

    I used this identity http://prntscr.com/7cuud8

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

    ok thanks

  28. 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.