a,
$A=\sin\Big(a-\dfrac{\pi}{4}\Big)\cos\Big(\dfrac{\pi}{3}-a\Big)+\cos\Big(a-\dfrac{\pi}{4}\Big).\sin\Big(\dfrac{\pi}{3}-a\Big)$
$=\sin\Big(a-\dfrac{\pi}{4}+\dfrac{\pi}{3}-a\Big)$
$=\sin\dfrac{\pi}{12}$
$=\dfrac{\sqrt6-\sqrt2}{4}$
b,
$B=\sin\Big( \dfrac{\pi}{2}-\dfrac{\pi}{3}+a\Big).\cos\Big( a+\dfrac{\pi}{4}\Big)+\cos\Big(a+\dfrac{\pi}{6}\Big).\cos\Big(a+\dfrac{\pi}{4}+\dfrac{\pi}{2}\Big)$
$=\sin\Big(a+\dfrac{\pi}{6}\Big)\cos\Big(a+\dfrac{\pi}{4}\Big)+\cos\Big(a+\dfrac{\pi}{6}\Big).\sin\Big(a+\dfrac{\pi}{4}\Big)$
$=\sin\Big(a+\dfrac{\pi}{6}+a+\dfrac{\pi}{4}\Big)$
$=\sin\Big(2a+\dfrac{5\pi}{12}\Big)$
