AmTran_Bus
Prove this trig identity
csc^4-csc^2=cot^4+cot^2
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AmTran_Bus
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lgbasallote
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look at the LHS...try factoring out csc^2 what do you get?
AmTran_Bus
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|dw:1353025247991:dw|
lgbasallote
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not exactly....if you factor out csc^2 then csc^4 becomes csc^2 but csc^2 doesn't become csc^2
lgbasallote
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AmTran_Bus
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Would it even exist, that is, would it cancel? Or just be csc?
lgbasallote
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what is csc^2/csc^2?
AmTran_Bus
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ohhhh. I feel dumb. Got ya.
lgbasallote
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so what should the factored form be?
AmTran_Bus
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|dw:1353025535036:dw|
lgbasallote
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right
lgbasallote
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now what is csc^2 - 1?
AmTran_Bus
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cot?
lgbasallote
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cot^2
lgbasallote
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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
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csc2 = 1/sin...it also equals cot+1
lgbasallote
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cot^2 + 1 not cot + 1
AmTran_Bus
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Sorry, your exactly right.
lgbasallote
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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
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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
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would the lhs say csc cot ^4? The RHS is cot^4 +cot^2
lgbasallote
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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
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Its not that I'm confused as much as tired my friend.
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lgbasallote
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well anyway... cot^2(cot^2 + 1) becomes cot^4 + cot^2
so you have just proven the identity
AmTran_Bus
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Thanks!!!!!!!
lgbasallote
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welcome