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This lecture covers the addition theorem for trigonometric functions, including formulas for double angles. It explains the unit vector, rotation of vectors, and the expressions for cosine and sine of the sum and difference of angles. The lecture also delves into the tangent of the sum, providing insights into when the tangent of the sum is valid. Additionally, it explores the cotangent of the sum and difference, as well as the sine, cosine, and tangent of double angles. Examples are provided to illustrate the application of these formulas.