Question

I don't believe that I solved this problem correctly...
(will post below)

Answer 1

\[\frac{ \cos2\theta }{ \cos \theta -\sin \theta}\]

Answer 2

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

Answer 3

I ended up with 0/0 meaning that the limit didn't exist, but I have a feeling I did this wrong.

Answer 4

Try the identity\[\cos 2\theta = \cos^2\theta - \sin^2\theta\]This can be factored and then the fraction can be simplified

Answer 5

Let me clarify... pi/4 = c not the limit.
Sorry about that.

Answer 6

\[\frac{\cos ^2\theta-\sin ^2\theta}{\cos \theta-\sin \theta}=\frac{(\cos \theta-\sin \theta)(\cos \theta+\sin \theta)}{\cos \theta-\sin \theta}\]

Answer 7

Then I would just cancel out the like terms in the numerator and the denominator, plug in my c values and solve?

Answer 8

That's right

Answer 9

Oh okay, thank you. :)
I guess I'll medal ospreytriple since they responded first? But I'll fan both of you. :)

Answer 10

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

Answer 11

Great to know! I'll keep that in mind next time I get it as an answer.