I'm sorry about the stupid questions, I just don't understand this.
Express these in surd form and rationalize the denominators
a)
$\displaystyle \frac{1}{1+cos45}$
Thank you so much!
you should know that $\displaystyle \cos 45^{\circ} = \frac {\sqrt {2}}{2}$
so, $\displaystyle \frac {1}{1 + \cos 45} = \frac {1}{1 + \frac {\sqrt {2}}{2}}$
$\displaystyle = \frac {1}{\frac {2 + \sqrt {2}}{2}}$
$\displaystyle = \frac {2}{2 + \sqrt {2}}$
Now we need to rationalize this. I don't want to do all the work for you, so i'll tell you what to do.
multiply by the conjugate of the base ($\displaystyle 2 - \sqrt {2}$) over itself, and simplify