Key Trigonometry MCQ Practice Questions for Class 10 Maths Preparation
FAQs on Class 10 Trigonometry MCQs: Chapter-wise Practice for 2025-26
1. What are the major types of important questions asked from CBSE Class 10 Maths Chapter 8, Introduction to Trigonometry, for the 2025-26 exams?
For the 2025-26 board exams, the important questions from Chapter 8 primarily fall into four categories:
- Calculating Ratios: Questions where one trigonometric ratio (like sin A) is given, and you need to find other ratios (like cos A, tan A).
- Standard Angle Evaluation: Problems that require you to substitute the values of trigonometric ratios for standard angles like 0°, 30°, 45°, 60°, and 90° into an expression and simplify.
- Trigonometric Identity Proofs: Questions that ask you to prove an identity, mainly using the fundamental identity sin²θ + cos²θ = 1 and its variations. These are often worth 3 marks.
- Simple Application Problems: Basic problems that can be represented by a right-angled triangle, where you need to use trigonometric ratios to find unknown sides or angles.
2. Which questions based on trigonometric ratios of standard angles are most expected in board exams?
Questions involving standard angles are a very common and important part of this chapter. You can expect the following types:
- Direct Evaluation: Problems where you must calculate the exact value of an expression, for example, find the value of 2 tan²45° + cos²30° – sin²60°.
- Solving for an Angle: Questions where an equation is given, and you need to find the value of an acute angle. For instance, if 2 sin 2θ = √3, find θ.
- Verification Problems: Questions where you need to verify a statement for given angles, such as verifying tan(A+B) = (tanA + tanB)/(1 - tanA tanB) for A=30° and B=30°.
3. What is the most important trigonometric identity for Class 10, and what kind of proof-based questions come from it?
The single most important identity for Class 10 is sin²A + cos²A = 1. All proof-based questions in the exam will revolve around applying this identity or its derived forms (1 - sin²A = cos²A and 1 - cos²A = sin²A). Important questions will require you to manipulate an expression on the Left-Hand Side (LHS) using algebraic rules and this identity to arrive at the Right-Hand Side (RHS). These are often 3-mark questions and test your logical step-by-step simplification skills.
4. How are marks typically allocated for important questions from Introduction to Trigonometry in the Class 10 board exam pattern?
Based on the CBSE exam pattern for the 2025-26 session, marks from this chapter are generally distributed as follows:
- 1-Mark Questions (MCQ/VSA): These test your knowledge of basic formulas, standard angle values, or finding a simple ratio. For example, 'If sin θ = cos θ, find the value of θ'.
- 2-Mark Questions (Short Answer): These may involve calculating all T-ratios when one is given or solving a simple identity.
- 3-Mark Questions (Short Answer): This is a very common weightage for proving trigonometric identities. These questions require multiple steps of logical simplification.
- Case-Study Questions (4 Marks): A real-world scenario might be described, which can be modelled using a right-angled triangle, followed by sub-questions on calculating trigonometric ratios or values.
5. Why are the identity-based 'Prove That' questions considered difficult, and what is the best strategy to solve them?
These questions are considered Higher Order Thinking Skills (HOTS) questions because they require more than just formula memorisation. They test your ability to apply algebraic manipulation alongside trigonometric rules. The path to the solution is not always obvious.
Here is a proven strategy:
- Start with the Complex Side: Always begin simplifying the more complicated side of the equation (usually the LHS).
- Convert to Sine and Cosine: A very effective technique is to convert all other ratios (tan, cot, sec, cosec) into their fundamental forms in terms of sin and cos.
- Use Algebra: Look for opportunities to use algebraic identities like (a+b)(a-b) = a²-b², or to take a common denominator.
- Aim for the Goal: Keep the other side of the equation in mind to guide your steps.
- Practice NCERT Exemplar: The NCERT Exemplar contains many high-quality proof questions that are excellent for board preparation.
6. How should I tackle important questions that combine trigonometry with algebraic identities?
These questions are designed to test your conceptual understanding. The key is to not see them as separate topics. First, simplify the expression using standard algebraic rules and identities like (a+b)², (a-b)², or a²-b². After the algebraic simplification, look for places to substitute the trigonometric identity sin²θ + cos²θ = 1. For example, if you encounter an expression like (1 - sin A)(1 + sin A), you should first simplify it algebraically to 1 - sin²A, and then use the trigonometric identity to convert it to cos²A.
7. What common mistakes should be avoided when solving important questions from Chapter 8 for the board exam?
To maximise your score, avoid these common errors:
- Ratio Confusion: Mixing up the definitions of sine, cosine, and tangent (SOH-CAH-TOA: Sine is Opposite/Hypotenuse, etc.).
- Angle Value Errors: Writing the wrong values for standard angles, like confusing sin 60° (√3/2) with cos 60° (1/2).
- Algebraic Mistakes: Incorrectly expanding brackets or making errors while finding the LCM of trigonometric terms.
- Conceptual Errors: A major mistake is assuming sin(A + B) is equal to sin A + sin B. This is fundamentally incorrect.
- Incomplete Proofs: In proof questions, you must show logical steps from the LHS to the RHS. Do not jump steps or assume the result.
