$VP=\dfrac{1}{\cos2x}-\tan2x$
$=\dfrac{1}{\cos2x}-\dfrac{\sin2x}{\cos2x}$
$=\dfrac{1-\sin2x}{\cos2x}$
$=\dfrac{\sin^2x-2\sin x\cos x+\cos^2x}{\cos^2x-\sin^2x}$
$=\dfrac{(\sin x-\cos x)^2}{(\cos x-\sin x)(\cos x+\sin x)}$
$=\dfrac{(\cos x-\sin x)^2}{(\cos x-\sin x)(\cos x+\sin x)}$
$=\dfrac{\cos x-\sin x}{\cos x+\sin x}$
$=VT$