$A=1+\sin x+\cos x+\sin 2x+\cos^2x-\sin^2x$
$=\sin x+\cos x+\sin 2x+2\cos^2x$
$=\sin x+\cos x+ 2\cos x (\sin x+\cos x)$
$=(\sin x+\cos x)(2\cos x+1)$
$B=\sin^3x\cos x-\cos^3x\sin x$
$=\sin x\cos x(\sin^2x-\cos^2x)$
$=-\sin x\cos x.\cos 2x$
$C=\sin^3x+\cos^3x-\cos2x$
$=(\sin x+\cos x)(1-\sin x\cos x)+\sin^2x-\cos^2x$
$=(\sin x+\cos x)(1-\sin x\cos x + \sin x-\cos x)$