AmTran_Bus
  • AmTran_Bus
Prove this trig identity csc^4-csc^2=cot^4+cot^2
Mathematics
katieb
  • katieb
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AmTran_Bus
  • AmTran_Bus
|dw:1353025115000:dw|
lgbasallote
  • lgbasallote
look at the LHS...try factoring out csc^2 what do you get?
AmTran_Bus
  • AmTran_Bus
|dw:1353025247991:dw|

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lgbasallote
  • lgbasallote
not exactly....if you factor out csc^2 then csc^4 becomes csc^2 but csc^2 doesn't become csc^2
lgbasallote
  • lgbasallote
|dw:1353025341525:dw|
AmTran_Bus
  • AmTran_Bus
Would it even exist, that is, would it cancel? Or just be csc?
lgbasallote
  • lgbasallote
what is csc^2/csc^2?
AmTran_Bus
  • AmTran_Bus
ohhhh. I feel dumb. Got ya.
lgbasallote
  • lgbasallote
so what should the factored form be?
AmTran_Bus
  • AmTran_Bus
|dw:1353025535036:dw|
lgbasallote
  • lgbasallote
right
lgbasallote
  • lgbasallote
now what is csc^2 - 1?
AmTran_Bus
  • AmTran_Bus
cot?
lgbasallote
  • lgbasallote
cot^2
lgbasallote
  • lgbasallote
so uou have \[\huge \csc^2 (\cot^2)\] now here comes a tricky part...review your identities and give me the equation for csc^2
AmTran_Bus
  • AmTran_Bus
csc2 = 1/sin...it also equals cot+1
lgbasallote
  • lgbasallote
cot^2 + 1 not cot + 1
AmTran_Bus
  • AmTran_Bus
Sorry, your exactly right.
lgbasallote
  • lgbasallote
you should check your notes and make sure you wrote them right....you might get them wrong... \[\huge \sin^2 + \cos^2 = 1\] \[\huge \tan^2 + 1 = \sec^2\] \[\huge \cot^2 + 1 = \csc^2\]
lgbasallote
  • lgbasallote
anyway...back to what i was saying... csc^2 is cot^2 + 1 so \[\huge \csc^2 (\cot^2) \implies (\cot^2 + 1)(\cot^2)\] now expand that
AmTran_Bus
  • AmTran_Bus
would the lhs say csc cot ^4? The RHS is cot^4 +cot^2
lgbasallote
  • lgbasallote
i think you're confused...let me flip it... \[\huge \cot^2 \theta (\cot^2\theta + 1)\] do you know how to distribute that now?
AmTran_Bus
  • AmTran_Bus
Its not that I'm confused as much as tired my friend. |dw:1353026333309:dw|
lgbasallote
  • lgbasallote
well anyway... cot^2(cot^2 + 1) becomes cot^4 + cot^2 so you have just proven the identity
AmTran_Bus
  • AmTran_Bus
Thanks!!!!!!!
lgbasallote
  • lgbasallote
welcome

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