**Biểu thức A:**
1. \( \cos \frac{5\pi}{3} \)
\[ \cos \frac{5\pi}{3} = \cos (2\pi - \frac{\pi}{3}) \]
\[ = \cos \frac{\pi}{3} \]
\[ = \frac{1}{2} \]

2. \( 2\tan \frac{\pi}{4} \)
\[ \tan \frac{\pi}{4} = 1 \]
\[ 2\tan \frac{\pi}{4} = 2 \]

3. \( \sin \frac{\pi}{3} \)
\[ \sin \frac{\pi}{3} = \sqrt{3}/2 \]

Tổng hợp:
\[ A = \frac{1}{2} + 2 - \frac{\sqrt{3}}{2} \]
\[ A = \frac{5 - \sqrt{3}}{2} \]

**Biểu thức B:**
1. \( \cot 60^\circ \)
\[ \cot 60^\circ = \frac{1}{\tan 60^\circ} \]
\[ = \frac{1}{\sqrt{3}} \]

2. \( \cos 450^\circ \)
\[ \cos 450^\circ = \cos (360^\circ + 90^\circ) \]
\[ = \cos 90^\circ = 0 \]

3. \( \sin 270^\circ \)
\[ \sin 270^\circ = -1 \]

Tổng hợp:
\[ B = \frac{1}{\sqrt{3}} + 0 - (-1) \]
\[ B = 1 + \frac{1}{\sqrt{3}} \]
Dùng công thức rationalize:
\[ B = 1 + \frac{\sqrt{3}}{3} \]
\[ B = \frac{4 + \sqrt{3}}{3} \]

Vậy:
\[ A = \frac{5 - \sqrt{3}}{2} \]
\[ B = \frac{4 + \sqrt{3}}{3} \]