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# Exercises The document contains a set of mathematical exercises related to trigonometry and angles. The exercises involve solving trigonometric equations, proving trigonometric identities, and finding angles. The problems are presented in a question-and-answer format with multiple parts (e.g., (...

# Exercises The document contains a set of mathematical exercises related to trigonometry and angles. The exercises involve solving trigonometric equations, proving trigonometric identities, and finding angles. The problems are presented in a question-and-answer format with multiple parts (e.g., (1), (2), (b), etc.). The text provides equations, diagrams (described below), and instructions to find solutions to the given problems. ## Diagrams The image contains a diagram of a circle with a quadrilateral inscribed within it. The quadrilateral is labeled as part of a larger figure. The lines within the quadrilateral extend from the circle. There is also a diagram of a right triangle with labeled sides and angles. These diagrams likely illustrate geometrical relationships relevant to the exercises. ## Examples of Problems Example 1: > (1) Find all angles between 0 and 360 that satisfy the equation sin 3x + 2cos x = 0 Example 2: > (1) Prove that sin(3α) = 4sin³(α) - 3sin(α) Example 3 (Diagram related): > (1) Prove that the perimeter of the rectangle is given by the equation P = 20sinθ + 10cosθ. The document primarily contains trigonometric problems involving finding angles, proving trigonometric identities, and solving trigonometric equations. Various forms of calculation are included, such as expanding, applying trigonometric formulas, and solving equations that include trigonometric functions.