[tex]\bf \cfrac{1}{cos(x)+1}+\cfrac{1}{cos(x)-1}=-2csc(x)cot(x)\\\\
-----------------------------\\\\
\cfrac{1}{cos(x)+1}+\cfrac{1}{cos(x)-1}\implies \cfrac{cos(x)-1+cos(x)+1}{[cos(x)+1][cos(x)-1]}\\\\
-----------------------------\\\\[/tex]
[tex]\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\
and\qquad sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\\\\
-----------------------------\\\\
\cfrac{cos(x)-1+cos(x)+1}{cos^2(x)-1}\implies \cfrac{cos(x)+cos(x)}{-[1-cos^2(x)]}
\\\\\\
\cfrac{2cos(x)}{-sin^2(x)}\implies -2\cdot \cfrac{1}{sin(x)}\cdot \cfrac{cos(x)}{sin(x)}[/tex]
and surely, you know what that is
