[tex]\sin(2x) \cdot (\hbox{tg} \ x+\hbox{ctg} \ x)=2[/tex]

tgx+ctgx=sinx/cosx+cosx/sinx=1/sinxcosx=2/sin2x

sin2x*(2/sin2x)=2

tg x + ctg x = sin x/cos x + cos x / sin x = (sin² x + cos² x)/(sin x * cos x) = 1 : sin 2x / 2 = 2 / sin 2x

sin 2x * 2 / sin 2x = 2

Истина