Extra Questions Of Trigonometry Class 10

Trigonometry is a critical topic in Class 10 mathematics that lays the foundation for various advanced mathematical concepts. It involves the study of the relationships between angles and sides in a triangle, especially right-angled triangles. Mastering trigonometry requires both conceptual understanding and extensive practice. Solving extra questions of trigonometry for Class 10 students enhances problem-solving skills and prepares them thoroughly for exams. These additional exercises help reinforce formulas, identities, and real-life applications while building confidence in the subject.

Importance of Practicing Extra Trigonometry Questions

Extra questions in trigonometry not only help students score higher in exams but also strengthen their grasp of fundamental concepts. These questions cover a variety of difficulties, from basic identity simplification to application-based word problems.

Why Practice Extra Questions?

• Improve understanding of trigonometric ratios
• Enhance skills in solving complex trigonometric identities
• Develop speed and accuracy for exams
• Prepare for application-based and higher-order thinking questions
• Boost confidence through consistent practice

Key Topics Covered in Class 10 Trigonometry

Before diving into the extra questions, students should be comfortable with the main topics of trigonometry included in the Class 10 syllabus. These form the basis for all advanced problems.

Important Concepts Include:

• Trigonometric Ratios (sine, cosine, tangent, secant, cosecant, cotangent)
• Trigonometric Identities
• Heights and Distances
• Relationship between sides and angles of right-angled triangles
• Complementary angles and values

Extra Trigonometry Questions for Practice

Basic Level Questions

These questions focus on basic understanding and formula application.

1. Find the value of sin 60°, cos 30°, and tan 45°.
2. If sin A = 3/5 and angle A is acute, find the values of cos A and tan A.
3. Evaluate: (sin² 30° + cos² 30°)
4. Prove that: tan² A + 1 = sec² A
5. Find the value of:
   • cot 60° – tan 30°
   • sec 45° + cosec 45°

Intermediate Level Questions

These problems involve application of trigonometric identities and simplification.

6. If tan A = 1/√3, find the values of sin A and cos A.
7. Prove that:
   • 1 + tan² A = sec² A
   • 1 + cot² A = cosec² A
8. Simplify: (1 + sin A)(1 – sin A) / cos² A
9. Evaluate:
   • sin 30° à cos 60° + sin 60° à cos 30°
10. Prove: (1 – tan A)(1 + tan A) = 1 – tan² A

Application-Based Questions

These questions require application of concepts to real-life or word problems, especially involving height and distance.

11. A ladder 10 m long is leaning against a wall. The ladder makes an angle of 60° with the ground. Find the height at which the top of the ladder touches the wall.
12. From a point on the ground, the angle of elevation of the top of a tower is 30°. If the height of the tower is 50 m, find the distance of the point from the base of the tower.
13. The angle of depression of a boat from the top of a cliff is 45°. If the height of the cliff is 100 m, find the distance of the boat from the base of the cliff.
14. The angles of elevation of the top of a tower from two points on the ground are 45° and 60°. The point at 45° is 30 m farther from the base than the point at 60°. Find the height of the tower.
15. A man observes the angle of elevation of the top of a tree to be 30°. He moves 20 meters closer and finds the angle to be 60°. Find the height of the tree.

Trigonometric Identities to Remember

Solving many of the above problems requires a solid memory of trigonometric identities. These are frequently used in simplifications and proofs.

Fundamental Identities:

• sin² A + cos² A = 1
• 1 + tan² A = sec² A
• 1 + cot² A = cosec² A

Value Table for Common Angles:

Students must memorize the trigonometric values for 0°, 30°, 45°, 60°, and 90° for all six functions.

Tips to Solve Trigonometry Problems Efficiently

Developing a strong approach and understanding patterns can make solving trigonometry questions easier and faster.

Helpful Strategies:

• Learn all standard values by heart and practice them regularly.
• Draw diagrams wherever possible, especially for height and distance problems.
• Use identities to simplify complex expressions before solving.
• Cross-check answers using calculators only after solving manually for verification.
• Attempt a variety of questions from sample papers and previous year papers.

Common Mistakes to Avoid

Many students make avoidable errors when solving trigonometric problems. Being aware of these can help improve accuracy.

• Confusing between sine and cosine functions
• Using incorrect identity or formula
• Wrongly substituting angle values (e.g., mixing up sin 60° and sin 30°)
• Not labeling triangles properly in word problems
• Skipping steps and making calculation errors

Practicing extra questions of trigonometry for Class 10 is an effective way to master this important math topic. By working on questions of various levels and types, students develop both conceptual clarity and problem-solving speed. From fundamental trigonometric identities to real-world applications involving heights and distances, consistent effort in solving these problems leads to better performance in exams and a strong foundation for higher studies. Students are encouraged to create a regular practice routine, use reference notes, and review solved examples to build confidence and accuracy in trigonometry.