Simplify each the following trigonometric expressions.  

1. $\cos\left(A\right)\cot\left(A\right) + \sin\left(A\right)$ 

   Hint (a):

   1. Rewrite everything in terms of sine and cosine.
   2. Get a common denominator.
   3. Use the Fundamental Pythagorean Identity.
   4. Simplify.

2. $\sin^2\left(θ\right)+\tan^2\left(θ\right)-\cot^2\left(θ\right)+\cos^2\left(θ\right)-\sec^2\left(θ\right)+\csc^2\left(θ\right)$ 

   Hint (b):

   Use the Pythagorean Identities.
   Change their forms to get $1$s.

   $\cos^{2}\left(θ\right) + \sin^{2}\left(θ\right) = 1$
   $1 + \tan^{2}\left(θ\right) = \sec^{2}\left(θ\right)$
   $1 + \cot^{2}\left(θ\right) = \csc^{2}\left(θ\right)$