b,
$VP=\dfrac{2\sin(x+y)}{\cos(x+y)+\cos(x-y)}$
$=\dfrac{2\sin(x+y)}{2\cos x\cos y}$
$=\dfrac{\sin(x+y)}{\cos x\cos y}$
$=\dfrac{\sin x\cos y+\sin y\cos x}{\cos x\cos y}$
$=\dfrac{\sin x}{\cos x}+\dfrac{\sin y}{\cos y}$
$=\tan x+\tan y$
$=VT$
a,
$VT=\sin(x+y)\sin(x-y)$
$=\dfrac{-1}{2}\left(\cos 2x-\cos2y\right)$
$=\dfrac{-1}{2}\left(1-2\sin^2x-1+2\sin^2y\right)$
$=\sin^2x-\sin^2y$
$=VP$