[tex]\it ctg 2x= \dfrac{cos 2x}{sin 2x} = \dfrac{cos62 x - sin^2 x}{2sin x cos x}= \dfrac{1}{2}\left(\dfrac{cos^2 x}{sin x cos x}-\dfrac{sin^2 x}{sin xcos x}\right)=
\\\;\\
= \dfrac{1}{2}\left(\dfrac{cos x}{sin x }-\dfrac{sin x}{cos x}\right) = \dfrac{1}{2}(ctg x - tg x)
[/tex]
