Giải thích các bước giải:
Ta có :
$\dfrac{\cos a+\sin a}{\cos a-\sin a}-\dfrac{\cos a-\sin a}{\cos a+\sin a}$
$=\dfrac{(\cos a+\sin a)^2}{(\cos a+\sin a)(\cos a-\sin a)}-\dfrac{(\cos a-\sin a)^2}{(\cos a+\sin a)(\cos a-\sin a)}$
$=\dfrac{\cos^2a+\sin^2a+2\cos a\sin a}{\cos^2a-\sin^2a}-\dfrac{\cos^2a+\sin^2a-2\cos a\sin a}{\cos^2a-\sin^2a}$
$=\dfrac{1+\sin2a}{\cos2a}-\dfrac{1-\sin2a}{\cos2a}$
$=\dfrac{1+\sin2a-(1-\sin2a)}{\cos2a}$
$=\dfrac{2\sin2a}{\cos2a}$
$=2\tan2a$
