$F=-\sin\Big(\dfrac{\pi}{2}-x\Big)+\cos(\pi-x)+\tan(2\pi+\dfrac{\pi}{2}-x\Big)-\tan\Big(\dfrac{\pi}{2}-x\Big)$
$=-\sin x-\cos x+\cot x-\cot x$
$=-\sin x-\cos x$
$H=\sin^2a(1+\cot a)+\cos^2a(1+\tan a)$
$=\sin^2a+\sin^2a.\cot a+\cos^2a+\cos^2a.\tan a$
$=\sin^2a+\sin a.\cos a+\cos a.\sin a+\cos^2a$
$=\sin^2a+2\sin a\cos a+\cos^2a$
$=(\sin a+\cos a)^2$