[tex]\bf sec\left( \frac{3\pi }{4} \right)\implies \cfrac{1}{cos\left( \frac{3\pi }{4} \right)}\implies \cfrac{1}{-\frac{\sqrt{2}}{2}}\implies -\cfrac{2}{\sqrt{2}}
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\textit{now, let's rationalize the denominator}
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-\cfrac{2}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies -\cfrac{2\sqrt{2}}{2}\implies \boxed{-\sqrt{2}}[/tex]
