Đáp án:
$\begin{array}{l}
3)\sin x.{\cos ^3}x - \cos x.{\sin ^3}x\\
= \sin x.\cos x\left( {{{\cos }^2}x - {{\sin }^2}x} \right)\\
= \sin x.\cos x.\cos 2x\\
= \frac{1}{2}.2\sin x.\cos x.\cos 2x\\
= \frac{1}{2}.\sin 2x.\cos 2x\\
= \frac{1}{4}.2\sin 2x.\cos 2x\\
= \frac{1}{4}.\sin 4x\\
7)\cot x + \tan x\\
= \frac{{\cos x}}{{\sin x}} + \frac{{\sin x}}{{\cos x}}\\
= \frac{{{{\cos }^2}x + {{\sin }^2}x}}{{\sin x.\cos x}}\\
= \frac{1}{{\sin x.\cos x}}\\
= \frac{2}{{2.\sin x.\cos x}} = \frac{2}{{\sin 2x}}
\end{array}$
