Rút gọn các biểu thức sau:

b) $B=\frac{\text{sin}4x}{1+\text{cos}4x}\cdot \frac{\text{cos}2x}{1+\text{cos}2x}-\text{cot}\left(\frac{3\pi }{2}-x\right)$ ;

b) $B=\frac{\text{sin}4x}{1+\text{cos}4x}\cdot \frac{\text{cos}2x}{1+\text{cos}2x}-\text{cot}\left(\frac{3\pi }{2}-x\right)$

 $=\frac{\text{2sin2}xcos2x}{{\text{2cos}}^2\text{2}x}\cdot \frac{\text{cos}2x}{{\text{2cos}}^{2}x}-\text{cot}\left(\pi +\frac{\pi }{2}-x\right)$     (áp dụng công thức góc nhân đôi)

$=\frac{\text{2sin}xcosx}{{\text{2cos}}^{2}x}-\text{cot}\left(\frac{\pi }{2}-x\right)$

$=\frac{\sin x}{\cos x}-\tan x=\tan x-\tan x=0$.