Verify the following trigonometric identities. Intermediate steps may involve complex fractions.

1. $\csc^{2} x + \sec^{2} x − \tan^{2} x −\cot^{2} x = 2$ 

   Hint (a):

   Fundamental Pythagorean Identities:
   $\sin^{2}θ + \cos^{2}θ = 1$
   $1 + \tan^{2}θ = \sec^{2}θ$
   $1 + \cot^{2}θ = \csc^{2}θ$

2. $\frac { \operatorname { sec } x - 1 } { 1 - \operatorname { cos } x } = \operatorname { sec } x$ 

   Hint (b):

   Change all terms to sine and cosine.