Use identities to simplify each expression.

$\displaystyle{\sin(x)+\frac{\cos^2(x)}{\sin(x)}}$ =
$\displaystyle{1-\frac{\sec^2(x)}{\tan^2(x)}}$ =
$\displaystyle{\frac{\tan^3(x)-\sec^2(x)\tan(x)}{\cot(-x)}}$ =