Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
VT = \frac{{\cos x + \sin x}}{{\cos x - \sin x}} - \frac{{\cos x - \sin x}}{{\cos x + \sin x}}\\
= \frac{{{{\left( {\cos x + \sin x} \right)}^2} - {{\left( {\cos x - \sin x} \right)}^2}}}{{\left( {\cos x - \sin x} \right)\left( {\cos x + \sin x} \right)}}\\
= \frac{{\left( {{{\cos }^2}x + 2\cos x.\sin x + {{\sin }^2}x} \right) - \left( {{{\cos }^2}x - 2\cos x.\sin x + {{\sin }^2}x} \right)}}{{{{\cos }^2}x - {{\sin }^2}x}}\\
= \frac{{4\cos x.\sin x}}{{{{\cos }^2}x - {{\sin }^2}x}}\\
= \dfrac{{\frac{{4\cos x.\sin x}}{{{{\cos }^2}x}}}}{{\frac{{{{\cos }^2}x - {{\sin }^2}x}}{{{{\cos }^2}x}}}}\\
= \dfrac{{4\frac{{\sin x}}{{\cos x}}}}{{1 - \frac{{{{\sin }^2}x}}{{{{\cos }^2}x}}}}\\
= \frac{{4\tan x}}{{1 - {{\tan }^2}x}} = VP
\end{array}\)
