what is the exact value of $\displaystyle sec\frac{\pi}{4}$ ?
thanks
$\displaystyle \sec \theta = \frac{1}{\cos \theta}$
$\displaystyle \therefore \sec \left(\frac{\pi}{4}\right) = \frac{1}{\cos \left(\frac{\pi}{4}\right)}$
We know that $\displaystyle \cos \frac{\pi}{4} = \frac{1}{\sqrt2}$
$\displaystyle \therefore \frac{1}{\left(\frac{1}{\sqrt2}\right)} = \sqrt2 = \sec \left(\frac{\pi}{4}\right) $