Rút gọn các biểu thức sau:
a) $B=\cos \left(\pi -x\right)+\sin \left(x-\frac{3\pi }{2}\right)-\tan \left(\frac{\pi }{2}+x\right)\cot \left(\frac{3\pi }{2}-x\right)$
b) $C=\frac{\sin (-4,8\pi ).\sin \left(-5,7\pi \right)}{\cot \left(-5,2\pi \right)}+\frac{\cos \left(-6,7\pi \right).\cos \left(-5,8\pi \right)}{\tan \left(-6,2\pi \right)}$

(AI giải đề cho tôi)
Câu 113. a) Ta có: $\cos (\pi -x)=-\cos x$; $\sin \left(x-\frac{3\pi }{2}\right)=\sin \left(-\left(\frac{3\pi }{2}-x\right)\right)=-\sin \left(\frac{3\pi }{2}-x\right)=-(-\cos x)=\cos x$; $\tan \left(\frac{\pi }{2}+x\right)=-\cot x$; $\cot \left(\frac{3\pi }{2}-x\right)=\tan x$. Do đó $\tan \left(\frac{\pi }{2}+x\right)\cot \left(\frac{3\pi }{2}-x\right)=-\cot x\cdot \tan x=-1$. Vậy $B=-\cos x+\cos x-(-1)=1$. b) Rút gọn từng góc: $\sin (-4,8\pi )=-\sin (4,8\pi )=-\sin (0,8\pi )=-\sin \frac{4\pi }{5}=-\sin \frac{\pi }{5}$; $\sin (-5,7\pi )=-\sin (5,7\pi )=-\sin (1,7\pi )=-\sin \frac{17\pi }{10}=-\sin \left(2\pi -\frac{3\pi }{10}\right)=\sin \frac{3\pi }{10}=\cos \frac{\pi }{5}$; $\cot (-5,2\pi )=-\cot (5,2\pi )=-\cot (1,2\pi )=-\cot \frac{6\pi }{5}=-\cot \frac{\pi }{5}$. Suy ra phân số thứ nhất $=\frac{\left(-\sin \frac{\pi }{5}\right)\cos \frac{\pi }{5}}{-\cot \frac{\pi }{5}}=\sin \frac{\pi }{5}\cos \frac{\pi }{5}\cdot \tan \frac{\pi }{5}={\sin }^2\frac{\pi }{5}$. Tương tự: $\cos (-6,7\pi )=\cos (6,7\pi )=\cos (0,7\pi )=\cos \frac{7\pi }{10}=-\sin \frac{\pi }{5}$; $\cos (-5,8\pi )=\cos (5,8\pi )=\cos (1,8\pi )=\cos \frac{9\pi }{5}=\cos \frac{\pi }{5}$; $\tan (-6,2\pi )=-\tan (6,2\pi )=-\tan (0,2\pi )=-\tan \frac{\pi }{5}$. Phân số thứ hai $=\frac{-\sin \frac{\pi }{5}\cos \frac{\pi }{5}}{-\tan \frac{\pi }{5}}={\sin }^2\frac{\pi }{5}$. Vậy $C=2{\sin }^2\frac{\pi }{5}$ (có thể viết $2{\sin }^{2}36^{\circ }$).