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anonymous

  • one year ago

I need complete help.. Complete the identity. Cos(a -b)/cos a cos b A. 1 + cot a cot b B. Tan a tan b + cot b C. 1 + tan a tan b D. 1 + cot a tan b

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  1. freckles
    • one year ago
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    try expanding the cos(a-b) part

  2. anonymous
    • one year ago
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    How? I look at my textbook, but it isn't helping me understand more.

  3. freckles
    • one year ago
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    then separate the fraction after the expansion do some canceling and finally just a little rewriting

  4. freckles
    • one year ago
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    you don't know the difference identity for cosine?

  5. anonymous
    • one year ago
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    No. My textbook never showed or told me.

  6. anonymous
    • one year ago
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    It just gives me problems to do and then I take my test.

  7. freckles
    • one year ago
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    sin(x-y)=sin(x)cos(y)-sin(y)cos(x) sin(x+y)=sin(x)cos(y)+sin(y)cos(x) cos(x+y)=cos(x)cos(y)-sin(x)sin(y) cos(x-y)=cos(x)cos(y)+sin(x)sin(y) so you never seen these identities? that is odd

  8. anonymous
    • one year ago
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    Correct. I am working hard to learn.. But I am confused.

  9. anonymous
    • one year ago
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    @freckles

  10. freckles
    • one year ago
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    yes?

  11. anonymous
    • one year ago
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    Can you help me a little better?

  12. freckles
    • one year ago
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    can you tell me if you applied that identity yet?

  13. anonymous
    • one year ago
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    Like, I am confused. I have done some sins, cos, and tans but not like this.

  14. freckles
    • one year ago
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    do you see the cos(a-b) on top?

  15. freckles
    • one year ago
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    do any of the identities I mentioned look like this on the left hand side?

  16. anonymous
    • one year ago
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    I do and yes.

  17. freckles
    • one year ago
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    well can you apply that identity then...

  18. freckles
    • one year ago
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    like can you expand cos(a-b)

  19. anonymous
    • one year ago
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    The expanding is the confusing part. Never done it.

  20. freckles
    • one year ago
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    so you don't see how cos(x-y) looks exactly like cos(a-b) except in the place of x we have a and in the place of y we have b?

  21. anonymous
    • one year ago
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    I see now.

  22. freckles
    • one year ago
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    replace the x and y on the right hand side with a and b respectively

  23. freckles
    • one year ago
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    and you have expanded cos(a-b)

  24. anonymous
    • one year ago
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    Okay. Is that all I do?

  25. freckles
    • one year ago
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    to expand cos(a-b) yes for the question you have asked here at the top, no

  26. freckles
    • one year ago
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    I actually gave a few more steps above after the expansion

  27. anonymous
    • one year ago
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    Okay. Thanks!

  28. freckles
    • one year ago
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    something about separating the fraction canceling stuff and rewriting a bit

  29. freckles
    • one year ago
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    can you show me what you have after rewriting \[\frac{\cos(a-b)}{\cos(a)\cos(b)}\]

  30. freckles
    • one year ago
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    or show me what you have for the numerator please

  31. anonymous
    • one year ago
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    Yes

  32. anonymous
    • one year ago
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    Cos(x-y)= cos(x) cos (y) I am still somewhat confused

  33. freckles
    • one year ago
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    ok well it looks like you didn't use the identity I mentioned above

  34. freckles
    • one year ago
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    cos(x-y)=cos(x)cos(y)+sin(x)sin(y)

  35. freckles
    • one year ago
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    cos(a-b)=?

  36. freckles
    • one year ago
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    |dw:1444190564321:dw|

  37. anonymous
    • one year ago
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    Uhhh, ??? Sorry.. I have no clue. I have never done a problem like this. Cos(x-y)

  38. freckles
    • one year ago
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    |dw:1444190659448:dw|

  39. freckles
    • one year ago
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    |dw:1444190692534:dw|

  40. anonymous
    • one year ago
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    Cos(x-y)= cos(x)cos(y) + sin(x)sin(y)

  41. freckles
    • one year ago
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    \[\frac{\cos(a-b)}{\cos(a)\cos(b)}=\frac{\cos(a)\cos(b)+\sin(a)\sin(b)}{\cos(a)\cos(b)}\] write as two fractions (separate the fraction)

  42. anonymous
    • one year ago
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    Okay. I am understanding a little more.

  43. anonymous
    • one year ago
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    So, 1 + cot a????

  44. anonymous
    • one year ago
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    @freckles

  45. freckles
    • one year ago
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    \[\frac{\cos(a) \cos(b)}{\cos(a) \cos(b)}=1\] and \[\frac{\sin(a) \sin(b)}{\cos(a) \cos(b)}=\frac{\sin(a)}{\cos(a)} \frac{\sin(b)}{\cos(b)}=...?\]

  46. anonymous
    • one year ago
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    It equals... I have no clue. I am trying.

  47. anonymous
    • one year ago
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    I thought it was 1

  48. freckles
    • one year ago
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    so you don't know what tan(x) equals in terms of sin(x) and cos(x)?

  49. anonymous
    • one year ago
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    I do.. Sort of.

  50. freckles
    • one year ago
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    then what does it equal?

  51. anonymous
    • one year ago
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    Tan a tan b?

  52. freckles
    • one year ago
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    tan(x)=tan(a)tan(b)?

  53. freckles
    • one year ago
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    or did you mean sin(a)/cos(a)=tan(a) and sin(b)/cos(b)=tan(b)?

  54. anonymous
    • one year ago
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    I meant that

  55. freckles
    • one year ago
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    ok great \[\frac{\cos(a) \cos(b)}{\cos(a) \cos(b)}=1\] while \[\frac{\sin(a) \sin(b)}{\cos(a) \cos(b)}=\frac{\sin(a)}{\cos(a)} \frac{\sin(b)}{\cos(b)}=\tan(a) \tan(b)\]

  56. anonymous
    • one year ago
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    I am on the right track?

  57. freckles
    • one year ago
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    we should be done

  58. freckles
    • one year ago
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    so I hope so :p

  59. anonymous
    • one year ago
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    So, it is c ?

  60. anonymous
    • one year ago
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    *?

  61. freckles
    • one year ago
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    yes that is what we got 1+tan(a)tan(b)

  62. anonymous
    • one year ago
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    Yay! Thank you, thank you!

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