Prove the trig identity: (1-cos θ)(1+cos θ)= 1/csc^2 θ

1. Start with the left side of the equation: (1 - \cos \theta)(1 + \cos \theta)

2. Apply the difference of squares formula:

(1 - \cos \theta)(1 + \cos \theta) = 1 - \cos^2 \theta

3. Use the Pythagorean identity:

1 - \cos^2 \theta = \sin^2 \theta

4. Relate to the right side:

\sin^2 \theta = \frac{1}{\csc^2 \theta}