Chứng minh đẳng thức sau :

$\frac{{1 + si{n^2}x}}{{1 - si{n^2}x}} = 1 + 2ta{n^2}x$

Có ${\sin ^2}x + {\cos ^2}x = 1 \Rightarrow 2{\sin ^2}x = 1 - {\cos ^2}x + {\sin ^2}x$

$\Rightarrow 1 + {\sin ^2}x = 2{\sin ^2}x + {\cos ^2}x$

$\Rightarrow VT = \frac{{2{{\sin }^2}x + {{\cos }^2}x}}{{{{\cos }^2}x}} = 2{\tan ^2}x + 1$.