Hello, I managed to get stuck on what looks to be a simple problem (again).


The problem in question was to solve for all possible values of x in the domain \(-\pi\leq x<\pi\) for the equation \(\cot(x) * \cos^2(x)=\cot(x)\).

I lumped all terms to the left and factored as it into this: \(\cot(x) * (\cos^2(x)-1)=0\)


Thus either \(\cot (x) = 0\) or \(\cos^2(x)=1\). From the former I got \(x=\pm{\pi\over2}\) and from the latter \(x=-\pi\) or \(0\). Of these, I thought I should eliminate \(-\pi\) and \(0\), since they both make the value of \(\cot(x)\) undefined. However, I then went to check my work with WolframAlpha, which presented all four answers as completely fine.


If someone could explain what I did wrong, it would help me a lot (this has been living in my head rent free for some time). Thanks in advance!

 Aug 20, 2023

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