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The document you uploaded contains multiple-choice, reasoning, and case-study-based questions on **Chapter 8: An Introduction to Trigonometry** for a Class X mathematics exam. Below is a summary of the types of questions it includes:

### Sample Multiple-Choice Questions (MCQs):
1. **Basic trigonometric identities and angle relationships** (e.g., \( \sin(2B) = 2\sin(B) \)).
2. **Trigonometric functions and values** for specific angles like 45°, 60°, 90°, etc.
3. **Trigonometric ratios** and their calculations in right-angled triangles (e.g., \( \tan A \), \( \sec A \)).
4. **Manipulations of trigonometric expressions** (e.g., finding the value of \( \cos^2 A + \sin^2 A \)).
   
### Case Study Examples:
1. **A crane problem** involving calculating distances and angles using trigonometry.
2. **A tree broken by a storm** where you apply the Pythagoras theorem to find the length of the broken part and height.
3. **Airplane travel distances** using the Pythagoras theorem to find the distance between two planes.
4. **Birdhouse project** using trigonometric ratios for triangular shapes.
5. **Sandwich triangle problem** involving calculating angles and using trigonometric identities.

### Assertion and Reasoning Questions:
These questions test logical understanding where you validate an assertion based on a reason provided (e.g., whether \(\sin A = \frac{3}{5}\) is possible given the properties of a right triangle).

Would you like to focus on solving any particular question from the document or need detailed explanations on specific topics?

### Five Follow-up Questions:
1. How do you solve a trigonometric equation like \( \sin 2B = 2 \sin B \)?
2. Can you explain how to calculate the height of the tree in the case study after a storm?
3. How is the distance between two airplanes calculated using the Pythagorean theorem?
4. What is the significance of the minimum and maximum values for trigonometric functions?
5. How would you solve for the angle of rotation in the crane problem using trigonometry?

### Tip:
Always check for standard trigonometric values (like \( \sin 30^\circ \), \( \cos 45^\circ \)) as they often simplify complex trigonometric expressions.

The document you uploaded contains multiple-choice, reasoning, and case-study-based questions on Chapter 8: An Introduction to Trigonometry for a Class X mathematics exam. Below is a summary of the types of questions it includes.

Explore Chapter 8 of Class X mathematics with a range of trigonometric questions, including multiple-choice, reasoning, and case studies. Topics include trigonometric identities, right-angled triangles, and the Pythagorean theorem, with problems on cranes, trees, and airplanes.

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