(cos(x)sin(x)^2)/(1-cos(x))=cos(x)+cos(x)^|2

$$\\ \frac{\cos(x)\sin^2(x)}{1-\cos(x)}=\cos(x)+\cos^2(x) \\\\ \text{Divide by cos(x)}\\ \frac{\sin^2(x)}{1-\cos(x)}=1+\cos(x) \\\\ \text{Multiply by 1-cos(x)}\\ \sin^2(x)=(1-\cos(x))(1+\cos(x))\\\\ \text{The right-hand side is the difference of two squares so}\\ \sin^2(x)=1-\cos^2(x)\\\\ \text{so:}\\ \sin^2(x)+\cos^2(x)=1\\ \text{which is correct!}$$

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