evaluate. write your answer in simplified, rationalized form. do not round. \nsec(π/4) =

Explanation:

Step1: Use the reciprocal identity

We know that (\sec\theta=\frac{1}{\cos\theta}). So, (\sec(\frac{\pi}{4})=\frac{1}{\cos(\frac{\pi}{4})}).

Step2: Find the value of (\cos(\frac{\pi}{4}))

The value of (\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}).

Step3: Substitute and simplify

Substitute (\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}) into (\sec(\frac{\pi}{4})=\frac{1}{\cos(\frac{\pi}{4})}), we get (\sec(\frac{\pi}{4})=\frac{1}{\frac{\sqrt{2}}{2}}). Using the rule (\frac{a}{\frac{b}{c}}=\frac{ac}{b}), then (\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}). Rationalize the denominator: (\frac{2}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\sqrt{2}).

Answer:

(\sqrt{2})