No simple way to derive them I'm afraid - more time and effort than you can afford to waste in a test.
Just write them down and/or memorise them.
$\displaystyle \displaystyle \sin{(\alpha \pm \beta)} = \sin{\alpha}\cos{\beta}\pm\cos{\alpha}\sin{\beta}$
$\displaystyle \displaystyle \cos{(\alpha \pm \beta)} = \cos{\alpha}\cos{\beta}\mp \sin{\alpha}\sin{\beta}$.
If I can memorise them you can too :P