Trouble Simplifying Homework Equations

[ACLerok]

Homework Statement

I am reviewing some old exam solutions and came across something I cannot figure out. I'm don't understand how they simplify from the first equation to the second. I looked up a table of trig identies but could not find anything that would help.

Homework Equations

http://img296.imageshack.us/img296/864/untitledimageda3.th.jpg

The Attempt at a Solution

 

[Gib Z]

Expand cos ( theta + pi/4), and times it by root 2.

 

[HallsofIvy]

The relevant trig identity is $cos(\theta+ \phi)= cos(\theta)cos(\phi)- sin(\theta)sin(\phi)$

Ignoring the 'm(t)' which just "goes along for the ride", you have $2cos(\theta)- 2 sin(\theta)$. Obviously, since 2> 1, there is no $\phi$ that has both sine and cosine equal to 2- you will need divide by something. But you would still have $cos(\phi)= sin(\phi)$. What value of $\phi$ has that property? And what do you then need to divide by?