Với $a\ne \dfrac{\pi}{2}+k\pi\quad(k\in\mathbb{Z})$:
$VT=\dfrac{\cos a+\sin a}{\cos^3a}$
$=\dfrac{\cos a}{\cos^3a}+\dfrac{\sin a}{\cos^3a}$
$=\dfrac{1}{\cos^2a}+\dfrac{\tan a}{\cos^2a}$
$=1+\tan^2a+\tan a(1+\tan^2a)$
$=\tan^3a+\tan^2a+\tan a+1$
$\ne VP$
Vậy không thể chứng minh.