2.
\(B=\cos x\sqrt{\frac{1}{1-\cos x}+\frac{1}{1+\cos x}}-\sqrt{2}\cot x\)
\(=\cos x\sqrt{\frac{2}{1-\cos ^2x}}-\sqrt{2}\cot x=\cos x\sqrt{\frac{2}{\sin ^2x}}-\sqrt{2}\cot x=\frac{\sqrt{2}\cos x}{|\sin x|}-\sqrt{2}\cot x\)
Nếu $\sin x>0$ thì: $B=\frac{\sqrt{2}\cos x}{\sin x}-\sqrt{2}\cot x=\sqrt{2}\cot x-\sqrt{2}\cot x=0$
Nếu $\sin x< 0$ thì $B=\frac{\sqrt{2}\cos x}{-\sin x}-\sqrt{2}\cot x=-\sqrt{2}\cot x-\sqrt{2}\cot x=-2\sqrt{2}\cot x$
3.
\(C=\sin ^3x+\cos^2x\sin x+\cos x\tan x=\sin x(\sin ^2x+\cos ^2x)+\cos x.\frac{\sin x}{\cos x}\)
\(=\sin x.1+\sin x=2\sin x\)
4.
\(D=\frac{\sin ^3a+\cos ^3a}{\cos ^2a+\sin a(\sin a-\cos a)}=\frac{(\sin a+\cos a)(\sin ^2a-\sin a\cos a+\cos ^2a)}{\cos ^2a+\sin ^2a-\sin a\cos a}=\sin a+\cos a\)
