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anonymous

  • one year ago

(_____)^2 = (csc x-1)(csc x+1) What is suppose to be in the blank? ***I know this is a trig identity and do not have my sheet with me. No online refrences are helping me***

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  1. anonymous
    • one year ago
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    I know it has to be either tan x or cot x. My memory is not on my side today.

  2. UsukiDoll
    • one year ago
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    ok.. there are three trig identities. the most common is \[\cos^2x+\sin^2x=1\]

  3. UsukiDoll
    • one year ago
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    but there are two more equations.

  4. anonymous
    • one year ago
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    Ok

  5. UsukiDoll
    • one year ago
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    \[1+\tan^2x=\sec^2x\] \[1+\cot^2x = \csc^2x \]

  6. UsukiDoll
    • one year ago
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    let's solve the right hand side of the equation to see who is the culprit lol xD so we expand \[(cscx-1)(cscx+1)\]

  7. anonymous
    • one year ago
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    Haha ok

  8. UsukiDoll
    • one year ago
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    just use foil ... you will notice that O and I cancel out

  9. anonymous
    • one year ago
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    Not familiar with FOIL (Sorry). My teacher calls it the "F word" (lol)

  10. UsukiDoll
    • one year ago
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    first outer inner last

  11. UsukiDoll
    • one year ago
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    \[(cscx-1)(cscx+1) = (cscx)(cscx)+(1)(cscx)+(-1)(cscx)+(1)(1)\]

  12. UsukiDoll
    • one year ago
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    fffffffff missed a sign on the last one should be +(-1)(1)

  13. anonymous
    • one year ago
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    Oh ok! I think I see what you are getting at

  14. UsukiDoll
    • one year ago
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    \[(cscx-1)(cscx+1) = (cscx)(cscx)+(1)(cscx)+(-1)(cscx)+(-1)(1) = (cscx)^2+cscx-cscx-1\]

  15. UsukiDoll
    • one year ago
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    OY ! \[(cscx)^2+cscx-cscx-1 \]

  16. UsukiDoll
    • one year ago
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    the cscx-cscx cancels out

  17. UsukiDoll
    • one year ago
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    \[\csc^2x-1\]

  18. anonymous
    • one year ago
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    Then we can add the 1 right?

  19. UsukiDoll
    • one year ago
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    do you remember \[1+\cot^2x = \csc^2x ? \]

  20. UsukiDoll
    • one year ago
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    what do I need to do have \[\cot^2x \] by itself

  21. anonymous
    • one year ago
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    Yep!

  22. anonymous
    • one year ago
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    subract the 1?

  23. UsukiDoll
    • one year ago
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    yes subtract on both sides..

  24. anonymous
    • one year ago
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    Oh ok! So we just proved that cot^2 (x) is my answer right?

  25. UsukiDoll
    • one year ago
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    yeah

  26. UsukiDoll
    • one year ago
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    \[\cot^2x = \csc^2x-1\]

  27. anonymous
    • one year ago
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    Would I just write it as cotx?

  28. UsukiDoll
    • one year ago
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    huh? you mean for (cotx)^2 = (csc^2x-1)

  29. anonymous
    • one year ago
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    Yes

  30. UsukiDoll
    • one year ago
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    hmmm... if you don't forget this part \[\cot^2x = \csc^2x-1 \]

  31. UsukiDoll
    • one year ago
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    \[(cotx)^2 = (cscx)^2-1\] means the same

  32. UsukiDoll
    • one year ago
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    just don't write cot2x and csc2x-1 BIG NO NO!

  33. anonymous
    • one year ago
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    Ok! Thank you for your time and teaching me!

  34. anonymous
    • one year ago
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    if u observe the RHS, u see it results csc^2-1 there is also an identity saying that, cosec^2-cot^2=1 that implies cosec^2-1=cot^2...therefore theRHS is cot^2 therefore obviously LHS must be cot^2...therefore the answer is cot

  35. UsukiDoll
    • one year ago
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    ^ done already lol

  36. UsukiDoll
    • one year ago
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    the term cosecant isn't used for the Pythagorean identities.

  37. UsukiDoll
    • one year ago
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    but there is one identity that is used beyond trig and that's the \[\cos^2x+\sin^2x = 1 \]

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