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skybunnygirl

  • one year ago

(1+cos3t)/(sin3t)+(sin3t)/(1+cos3t)=2csc3t

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  1. Hoa
    • one year ago
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    \[\frac{ 1+\cos3t }{ \sin3t }+\frac{ \sin3t }{ 1+\cos3t }= 2\csc3t\] what do you want? prove it?

  2. skybunnygirl
    • one year ago
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    yes please, im having the hardest time with these questions...

  3. Hoa
    • one year ago
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    I give you idea, you do the rest. the first part \[\frac{ 1+\cos3t }{ \sin3t }= \frac{ 1 }{ \sin3t }+ \frac{ \cos3t }{ \sin3t }= \csc 3t + \cot 3t\]

  4. skybunnygirl
    • one year ago
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    ok let me look at it

  5. skybunnygirl
    • one year ago
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    no go, have no idea what is next

  6. Zebo
    • one year ago
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    That is pretty much it. You know what cot(x) is equal to? Also what is csc(x) equal to.

  7. skybunnygirl
    • one year ago
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    cotx=1/tanx

  8. skybunnygirl
    • one year ago
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    cscx=1/sinx

  9. Zebo
    • one year ago
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    what else for cotx? there should be one more

  10. skybunnygirl
    • one year ago
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    cosx/sinx

  11. Zebo
    • one year ago
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    now look at the first step, do you see something similar to what you said

  12. skybunnygirl
    • one year ago
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    sorry you lost me...

  13. Zebo
    • one year ago
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    you said cotx = cosx/sinx and you said cscx=1/sinx right?

  14. skybunnygirl
    • one year ago
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    yes and that is what we converted into part of the original problem

  15. Hoa
    • one year ago
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    ok I give you mine : from yours , right side = 2/ sin3t. write it out

  16. Hoa
    • one year ago
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    now I just prove that left side * sin 2t =2, right? it is easy to do

  17. Hoa
    • one year ago
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    \[\sin 3t \left[ \frac{ 1 + cost 3t }{ \sin3t } +\frac{ \sin3t }{ 1 + \cos 3t } \right]\]

  18. Hoa
    • one year ago
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    \[= \frac{ \sin 3t + \cos 3t }{ \sin3t }+ \frac{ \sin^2 3t }{ 1 + \cos 3t }\]

  19. skybunnygirl
    • one year ago
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    ok, how did we get from csc3t+cot3t+sin3t/1+cos3t to what you writing now?

  20. Hoa
    • one year ago
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    \[= (\frac{ sint }{ \sin3t }+ \frac{ \sin3tcos3t }{ \sin3t }+ \frac{ 1-\cos^2 3t }{1+\cos 3t })\]

  21. Hoa
    • one year ago
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    \[=1+ \cos 3t + \frac{ (1+\cos3t)(1-\cos3t) }{ 1+\cos 3t }\]

  22. Hoa
    • one year ago
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    and then you have 1+1 =2. the proof done. is it clear?

  23. Hoa
    • one year ago
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    I make the right side2 csc 3t = 2/ sin3t. and then time both sides to sin 3t

  24. Hoa
    • one year ago
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    do you get mine? think of it. write out and it will make sense to you.

  25. skybunnygirl
    • one year ago
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    ok let me look at it and see, im still not sure why we did the very first step as we ended up working out the original set up

  26. Hoa
    • one year ago
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    our goal is prove the original equation is true, that means you must prove the left side = right side. some equation is not true at all, for example : how can you prove 1+1 =3? fortunately, your problem is prove it true, that means it is true already, just explain in which logic, it is true. done

  27. skybunnygirl
    • one year ago
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    ok, let me work it out on paper and see what I come up with. Thanks for your help.

  28. Hoa
    • one year ago
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    you are welcome

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