$E=(1+\frac{\cos^{2} x}{\sin^{2} x})\cdot (\sin^{2} x)$ $=$ $\sin^{2} x$ $+$ $\cos^{2} x$ $=$ $1$ Alternativa $\mathbb {D}$

$E = (1 + \cotg^2x)(1 - \cos^2x) = \left(1 - \dfrac{\cos^2x}{\sin^2x}\right)(\sin^2x)$ $= \left(\dfrac{\sin^2x + \cos^2x}{\sin^2x}\right)(\sin^2x) = \boxed{E = 1}$