# What is 2sin(theta/2-pi/4)-cos(theta/2) in terms of trigonometric functions of a unit theta?

$2 \sin \left(\frac{\theta}{2} - \frac{\pi}{4}\right) - \cos \left(\frac{\theta}{2}\right)$
$= 2 \left(\sin \left(\frac{\theta}{2}\right) \cos \left(\frac{\pi}{4}\right) - \sin \left(\frac{\pi}{4}\right) \cos \left(\frac{\theta}{2}\right)\right) - \cos \left(\frac{\theta}{2}\right)$
$= \sqrt{2} \sin \left(\frac{\theta}{2}\right) - \sqrt{2} \cos \left(\frac{\theta}{2}\right) - \cos \left(\frac{\theta}{2}\right)$
$= \sqrt{2} \sin \left(\frac{\theta}{2}\right) - \left(1 + \sqrt{2}\right) \cos \left(\frac{\theta}{2}\right)$