Răspuns :

tg x-ctg x=-2ctg 2x,   tg x-ctg x=-2 cos2x/sin 2x=> tg x-ctg x=-2 (cos²x-sin²x)/2sinxcosx ,=>tg x-ctg x=-cos²x/sin x cos x+sin²x/sin x cos x
tg x -ctg x=-cos x /sin x+sin x/cos x=>tg x-ctg x=-ctg x+tg x=>
egalitatea se vede imediat