f,
$B=\dfrac{1+2\cos^2x-1+\sin2x}{1-(1-2\sin^2x)+\sin2x}$
$=\dfrac{2\cos^2x+\sin2x}{2\sin^2x+\sin2x}$
$=\dfrac{2\cos^2x+2\sin x\cos x}{2\sin^2x+2\sin x\cos x}$
$=\dfrac{2\cos x(\cos x+\sin x)}{2\sin x(\sin x+\cos x)}$
$=\dfrac{\cos x}{\sin x}$
$=\cot x$
g,
$H=\tan(-x).\cot(x-\pi)+\cos(\pi+x)+2\sin\Big( \dfrac{\pi}{2}-x\Big)+\sin(-x).\tan\Big(\dfrac{\pi}{2}-x\Big)$
$=-\tan x.(-\cot(\pi-x))-\cos x+2\cos x-\sin x.\cot x$
$=\tan x.\cot(\pi-x)+2\cos x-\cos x-\cos x$
$=-\tan x.\cot x$
$=-1$
