deletions | additions       diff --git a/section_Q4_subsection_a_subsubsection__.tex b/section_Q4_subsection_a_subsubsection__.tex  index b91ef20..7781b1e 100644  --- a/section_Q4_subsection_a_subsubsection__.tex  +++ b/section_Q4_subsection_a_subsubsection__.tex 
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\subsubsection{Lemma 1}  Claim: \textbf{Claim}:  $\tau \in (0,2\pi/7)$. Pf: \textbf{Pf}:  From problem definition/assumed finite k we have $\tau > 0$. Additionally: $k=\lceil 2\pi/ \tau \rceil > 8 \implies 2\pi/ \tau > 7 \iff \tau < 2\pi/7$ 
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\subsubsection{Lemma 2}  Claim: \textbf{Claim}:  $\frac{1}{\cos x - \sin x}$ is monotone decreasing for $x\in (0, 2\pi/7)$. Pf: \textbf{Pf}:  $\frac{d(\cos x - \sin x)}{dx}=-(\sin x + \cos x) < 0$ for $x\in (0, \pi/4)$ therefore $\cos x - \sin x$ is monotone decreasing on this domain. As such, $\frac{1}{\cos x - \sin x}$ is monotone increasing.