1. The problem asks for three common applications of trigonometric identities and how to create steps to prove these identities using a flowchart. 2. Three common applications of trigonometric identities are: 1. Simplifying expressions involving trigonometric functions. 2. Solving trigonometric equations in physics and engineering. 3. Computing unknown sides or angles in triangles using laws such as sine and cosine laws. 3. To prove trigonometric identities using a flowchart, follow these learner-friendly steps: 1. **Understand the identity** you want to prove. 2. **Write down both sides** of the equation clearly. 3. **Manipulate one side** (usually the more complex side) using known identities such as Pythagorean identities, angle sum formulas, or double angle formulas. 4. **Simplify each step carefully**, showing intermediate transformations like factoring, combining fractions, or applying formulas. 5. **Repeat manipulation and simplification** until the side matches the other side of the identity. 6. **Conclude the proof** by stating both sides are equal. These steps help organize the logical flow of proving identities clearly and thoroughly.