deletions | additions       diff --git a/section_Q4_subsection_a_subsubsection__.tex b/section_Q4_subsection_a_subsubsection__.tex  index 4cbd17e..d0b44f4 100644  --- a/section_Q4_subsection_a_subsubsection__.tex  +++ b/section_Q4_subsection_a_subsubsection__.tex 
...
t\cdot|uv| &\geq |uw| + t\cdot|wv| \\  \iff t &\geq \frac{|uw|}{|uv|-|wv|} \\\\  LHS &\geq \frac{1}{\cos \tau - \sin \tau} \\  &\geq \frac{1}{\cos \angle_{vuw} - \sin \angle_{vuw} } \qquad \text{as $\angle_{vuw} \in (0,\tau$) + (0,\tau]$  (1)(2)}\\ &=\frac{|uv|}{|uw|-|wv|}\\  &\geq\frac{|uw|}{|uv|-|wv|} \qquad \text{as $|uv| > |uw|$}\\  &=RHS \ \ \square