$VT=2(\sin^6\alpha+\cos^6\alpha)+1$
$=2[(\sin^2\alpha)^3+(\cos^2\alpha)^3]+1$
$=2(\sin^2\alpha+\cos^2\alpha)(\sin^4\alpha+\cos^4\alpha-\sin^2\alpha\cos^2\alpha)+1$
$=2\sin^4\alpha+2\cos^4\alpha-2\sin^2\alpha\cos^2\alpha+(\sin^2\alpha+\cos^2\alpha)^2$
$=2\sin^4\alpha+2\cos^4\alpha-2\sin^2\alpha\cos^2\alpha+\sin^4\alpha+2\sin^2\alpha\cos^2\alpha+\cos^4\alpha$
$=3\sin^4\alpha+3\cos^4\alpha$
$=3(\sin^4\alpha+\cos^4\alpha)$
$=VP$
