anonymous
  • anonymous
I don't believe that I solved this problem correctly... (will post below)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\frac{ \cos2\theta }{ \cos \theta -\sin \theta}\]
anonymous
  • anonymous
I know that \[\cos2 \theta = 1-2\sin^2\] so I changed that to the numerator, and then plugged in my limit into the thetas, which is pi/4
anonymous
  • anonymous
I ended up with 0/0 meaning that the limit didn't exist, but I have a feeling I did this wrong.

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anonymous
  • anonymous
Try the identity\[\cos 2\theta = \cos^2\theta - \sin^2\theta\]This can be factored and then the fraction can be simplified
anonymous
  • anonymous
Let me clarify... pi/4 = c not the limit. Sorry about that.
Mertsj
  • Mertsj
\[\frac{\cos ^2\theta-\sin ^2\theta}{\cos \theta-\sin \theta}=\frac{(\cos \theta-\sin \theta)(\cos \theta+\sin \theta)}{\cos \theta-\sin \theta}\]
anonymous
  • anonymous
Then I would just cancel out the like terms in the numerator and the denominator, plug in my c values and solve?
anonymous
  • anonymous
That's right
anonymous
  • anonymous
Oh okay, thank you. :) I guess I'll medal ospreytriple since they responded first? But I'll fan both of you. :)
anonymous
  • anonymous
not to butt in but if you get \[\frac{0}{0}\] it does NOT mean the limit doesn't exist it means you have to do more work
anonymous
  • anonymous
Great to know! I'll keep that in mind next time I get it as an answer.

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