Giải thích các bước giải:
Ta có:
$\dfrac{\tan^3a}{\sin^2a}-\dfrac{1}{\sin a\cos a}+\dfrac{\cot^3a}{\cos^2a}$
$=\dfrac{\tan^3a(\sin^2a+\cos^2a)}{\sin^2a}-\dfrac{\sin^2a+\cos^2a}{\sin a\cos a}+\dfrac{\cot^3a(\sin^2a+\cos^2a)}{\cos^2a}$
$=\tan^3a(1+\dfrac{\cos^2a}{\sin^2a})-(\dfrac{\sin a}{\cos a}+\dfrac{\cos a}{\sin a})+\cot^3a(\dfrac{\sin^2a}{\cos^2a}+1)$
$=\tan^3a(1+\cot^2a)-(\tan a+\cot a)+\cot^3a(\tan^2a+1)$
$=\tan^3a+\tan^3a\cot^2a-(\tan a+\cot a)+\cot^3a\tan^2a+\cot^3a$
$=\tan^3a+\tan a(\tan a\cot a)^2-(\tan a+\cot a)+\cot a(\cot a\tan a)^2+\cot^3a$
$=\tan^3a+\tan a-(\tan a+\cot a)+\cot a+\cot^3a$
$=\tan^3a+\cot^3a$
