Verifying Trigonometric Identities

I'm a bit confused on verifying trigonometric identities. An example problem would be:

$\displaystyle \cos(\frac{\pi}{2})-\Theta=\sin\Theta$

Or:

$\displaystyle \cot(\pi+\Theta)=\cot\Theta$

Can someone please explain what exactly the question is asking, and how I find the solution? Thanks.

Also, is there any way to visually differ between the graph of a sine function and the graph of a cosine function, if you don't know if one may be shifted? Sorry if that is hard to understand.