[tex]\bf cot(x)+sin(x)=\cfrac{1+cos(x)-cos^2(x)}{sin(x)}\\\\
-----------------------------\\\\
\textit{now, recall your pythagorean identities}
\\\\
sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\\\\
-----------------------------\\\\
thus\qquad \cfrac{1+cos(x)-cos^2(x)}{sin(x)}\implies \cfrac{\boxed{1-cos^2(x)}+cos(x)}{sin(x)}
\\\\\\
\cfrac{\boxed{sin^2(x)}+cos(x)}{sin(x)}\implies \cfrac{sin^2(x)}{sin(x)}+\cfrac{cos(x)}{sin(x)}\implies\cfrac{cos(x)}{sin(x)}+ \cfrac{sin^2(x)}{sin(x)}
\\\\
[/tex]
[tex]\bf cot(x)+sin(x)[/tex]
