Use two triangles to evaluate the tangent sum formula

The video tutorial covers the analysis of two angles, U and V, using trigonometric concepts. It begins with a review of expressions from previous chapters, focusing on sine and cosine values. The tutorial explains the significance of Pythagorean triples, particularly the 3-4-5 triangle, and their application in determining the quadrant of angles. The analysis of triangle V is detailed, highlighting the conditions for tangent positivity. Finally, the video demonstrates the calculation of the tangent of U + V, emphasizing the importance of understanding complex fractions and rationalizing denominators.

What are the values of the sides of the triangle associated with angle V, and how are they determined?

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What is the common denominator used when simplifying the fractions in the tangent formula?

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How do you rationalize the denominator in the context of this problem?

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