The discussion focuses on the demonstration of the trigonometric identity cos²(x) = 1/(1 + tan²(x)). Participants emphasize the importance of understanding the definitions of tangent and sine, with one suggesting to substitute tan(x) = sin(x)/cos(x) into the equation. Simplifying the right-hand side leads to the identity cos²(x) + sin²(x) = 1, which is fundamental in trigonometry. The conversation highlights the need for foundational knowledge in trigonometric functions to grasp the demonstration effectively. Ultimately, the participants aim to collaboratively derive the formula through simplification and understanding of trigonometric identities.