Giải thích các bước giải:
$VT=\dfrac{(1+\sin^2a)(\sin a+\cos a)}{\cos^3a}\\
=\dfrac{\sin a+\cos a+\sin^3a+\sin^2a\cos a}{\cos^3a}\\
=\dfrac{\sin a}{\cos^3a}+\dfrac{\cos a}{\cos^3a}+\dfrac{\sin^3a}{\cos^3a}+\dfrac{\sin^2a\cos a}{\cos^3a}\\
=\tan a\dfrac{1}{\cos^2a}+\dfrac{1}{\cos^2a}+\tan^3a+\dfrac{\sin^2a}{\cos^2a}\\
=\tan a(1+\tan^2a)+1+\tan^2a+\tan^3a+\tan^2a\\
=\tan a+\tan^3a+1+2\tan^2a+\tan^3a\\
=2\tan^3a+2\tan^2a+\tan a+1=VP\Rightarrow ĐPCM$
