Chứng minh đẳng thức: (1 + sin x)(cot x – cos x) = cos³ x.

\[\left( {1 + sinx} \right)\left( {\cot x--cosx} \right)\]

\[ = (1 + \sin x)(\frac{{\cos x}}{{\sin x}} - \cos x)\]

\[ = \cos x(1 + \sin x).\frac{{1 - \sin x}}{{\sin x}}\]

\[ = \frac{{\cos x(1 - {{\sin }^2}x)}}{{\sin x}} = \frac{{\cos x.{{\cos }^2}x}}{{\sin x}} = \frac{{{{\cos }^3}x}}{{\sin x}}\]

Vậy (1 + sin x)(cot x – cos x) = cos³ x.