$VT=\dfrac{\cos(a+b).\cos(a-b)}{\cos^2a\cos^2b}$
$=\dfrac{\dfrac{1}{2}.\Big(\cos2a+\cos2b\Big)}{\cos^2a\cos^2b}$
$=\dfrac{\dfrac{1}{2}\Big( 2\cos^2a-1+2\cos^2b-1\Big) }{\cos^2a\cos^2b}$
$=\dfrac{\cos^2a+\cos^2b-1}{\cos^2a\cos^2b}$
$=\dfrac{ \cos^2a}{\cos^2a\cos^2b}+\dfrac{\cos^2b}{\cos^2a\cos^2b}-\dfrac{1}{\cos^2a\cos^2b}$
$=1+\tan^2b+1+\tan^2a-(1+\tan^2a)(1+\tan^2b)$
$=\tan^2a+\tan^2b+2-(1+\tan^2a+\tan^2b+\tan^2a\tan^2b)$
$=1-\tan^2a\tan^2b$
$=VP$