[tex]\bf \textit{difference and sum of cubes}
\\\\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
(a+b)(a^2-ab+b^2)= a^3+b^3
\\\\
a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad
(a-b)(a^2+ab+b^2)= a^3-b^3\\\\
-------------------------------\\\\
\cfrac{1+cot^3(x)}{1+cot(x)}+cot(x)=1+cot^2(x)
\\\\\\
\cfrac{1^3+cot^3(x)}{1+cot(x)}+cot(x)=1+cot^2(x)\\\\
-------------------------------\\\\
\cfrac{\underline{[1+cot(x)]}~~[1^2-[1cot(x)]+cot^2(x)]}{\underline{1+cot(x)}}+cot(x)
\\\\\\
1-cot(x)+cot^2(x)+cot(x)\implies 1+cot^2(x)[/tex]
