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Oh yes, I meant the latter. Sorry for the confusion that it may have lead to.

I'm not sure how to simplify this without spending a lot of time on it. Is there a pattern that I need to weed out?

Yes, thank you for letting me know. I had issues with a previous thread where I did not give enough information (where I thought I had). Also, since you mention it, I do have a lot of difficulty with identities. I just went back through my notes and realized that I had derived this formula...

It appears that I needed to use $$ \begin{array}{l} \cos ^{2}(\theta)=\frac{1+\cos (2 \theta)}{2} \\ \sin ^{2}(\theta)=\frac{1-\cos (2 \theta)}{2} \end{array} $$ To get the values of cos and sin in the solution. I was not familiar with this formula :nb).

Thank you for your replies. It seems that in trying to post only the relevant parts of the question, I am missing possibly essential information (that I am not picking up myself). The question in its entirety is: Reduce to standard form and graph the curve whose equation is ##x^{2}+4 x y+4...

So I get that: $$ \sin 2 \theta=-\frac{4}{5} $$ $$ \cos 2 \theta=-\frac{3}{5} $$ But what is the next step?

Oh right, I wasn't even thinking about infinity, I was just thinking of it as "undefined" Also, is this also correct? ##\begin{array}{l} \cot 2 \theta=0 \\ \frac{\cos 2 \theta}{\sin 2 \theta}=0 \\ \cos 2 \theta=0 \\ 2 \theta=90 \end{array}##

One of my solutions had this in one part. Why is this the case?