Simplifying a trigonometric expression by factoring out a GCF

The video tutorial explores a trigonometric problem involving cosine squared and cotangent. The teacher discusses initial strategies, such as converting to sines and cosines, and highlights the challenges faced, including dead ends. Alternative methods are considered, including using Pythagorean identities and factoring. The final simplification leads to the solution, emphasizing the importance of exploring different approaches and not assuming completion after a few steps.

How does the Pythagorean identity relate to the expression 'one plus cotangent squared'?

What is the final expression derived from the simplification process discussed in the text?