Three part problem:
To verify any given identity, it is often best to manipulate one side of the equation using logical steps until it is transformed into the other side of the formula. (This type of thinking is reflective of the way you might also solve any logical problem in real life. Indeed, showing that certain raw products input into a manufacturing process lead to a desired output doesn't allow for you to cancel inputs with outputs to get something like 1=1). In this multi-part problem, we will use algebra starting with one side and moving to the other to verify the identity

To get started, it is often best to start with the "worst" side...that is, the side that looks like it can really use some simplification. For this problem, the $\csc(t)$ looks pretty small so lets focus on the left side.

$\cos(t) \cot(t) + \sin(t) = \cos(t) \cdot$ $/ \sin(t) + \sin(t)$