[tex]\it ctgx = \dfrac{cosx}{sinx} = \sqrt{\dfrac{cos^2x}{sin^2x}} =\sqrt{\dfrac{1-sin^2x}{sin^2x}} =\sqrt{\dfrac{1-\dfrac{9}{25}}{\dfrac{9}{25}}} =
\\\;\\ \\\;\\
\sqrt{\dfrac{\dfrac{16}{25}}{\dfrac{9}{25}}} = \sqrt{\dfrac{16}{9}} = \dfrac{4}{3}[/tex]
