Hi. One of my math books seems to indicate that

$\displaystyle \sqrt {2 - 2\,sin\,t\,sin\,5t - 2\,cos\,t\,cos\,5t$

is equal to

$\displaystyle \sqrt {2 - 2\,cos\,4t}$

The transformation is I imagine quite obvious to everyone else, but if somebody could bear with me and show the hidden steps, it would help my learning.