CBSE Class 10 Maths 2024-25: Chapter 8 Introduction to Trigonometry Important Competency-Based Questions with Answers; Download Free PDF

As the CBSE Class 10 board exams get closer, it’s important for students to understand the new exam pattern. Starting in the 2024-25 school year, CBSE will include 50% more competency-based questions. These questions will be both multiple choice and written, focusing on how to use what students have learned in real-life situations.

This article explores Chapter 8 Introduction to Trigonometry. It highlights key competency-based questions and provides answers to help students succeed.

Understanding Competency-Based Questions in Chapter 8 Introduction to Trigonometry

Competency-based questions are designed to see how well students can apply their knowledge in everyday life. They can come in different forms, such as case studies, true-false questions, gap-filling tasks, and long or short answer questions.

Competency-based questions in Chapter 8: Introduction to Trigonometry go beyond memorization, encouraging critical thinking and problem-solving. These questions help students grasp concepts deeply by applying them to real-world scenarios.

CBSE Class 10 Maths Chapter 8: Introduction to Trigonometry Important Competency-Based Questions

Multiple Choice Questions

Q.1 Given, cot θ = 3, what is the value of cos θ?

Answer. (3)

Q.2 Given below is ΔPQR, right-angled at Q.

Answer. (2)

Q.3 

Answer. (2)

Q.4 If cot 81° = tan θ, what is the value of sec 5θ?

Answer. (3)

Q.5 Any relation which is ALWAYS true is an identity. Which of the following is a trigonometric identity?

1. only i) and ii)
2. only i) and iii)
3. only i), ii) and iii)
4. only i), iii) and iv)

Answer. (2)

Q.6 

1. only Q and R
2. only Q and S
3. only Q, R and S
4. all - P, Q, R and S

Answer. (1)

Q.7

1. sec θ + tan θ
2. sec θ - tan θ
3. sec² θ + tan² θ
4. (sec θ + tan θ)²

Answer. (1)

Q.8 

Answer. (4)

Free Response Questions

Q.9 If tan x - cot y = 0, find the value of x + y.

Show your steps.

(Note: 0° ≤ x, y ≤ 90°.)

Answer. Rewrites that the given equation as tan x = cot y

Concludes that this is only possible for a pair of complementary angles. Hence, x + y = 90 °

Q.10 Prove that:

sin ² 70° - sin ² 10° = cos ² 10° - cos ² 70°

Answer. Proceeds with LHS as, 
= sin² 70° - sin² 10°

Uses identity sin² θ = 1 - cos² θ to get

= (1 - cos ² 70°) - (1 - cos² 10°)
= 1 - cos ² 70° - 1 + cos² 10°
= cos² 10° - cos² 70° = RHS

Q.11 Write true or false for the given statement and give a valid reason.
In ΔABC, right-angled at B, cosec A can be less than 1.

Answer. Writes False.

Gives a reason. For example, writes that as, in a right-angled triangle, cosec A is always greater than or equal to 1, as it represents the reciprocal of the sine function, and the sine of an acute angle is always less than or equal to 1.

Q.12 What is the value of sin ² θ + sec ² θ + cos ² θ - tan ² θ where θ is an acute angle? Show your work.

Answer. Rearranges the given expression and uses identities to evaluate as:

(sin ² θ + cos ² θ) + (sec ² θ - tan ² θ)
= 1 + 1 = 2

Case-Based Questions

Study the given information and answer the questions that follow.

Shown below is the rough figure of the side view of a proposed water slide which has to be constructed in a water park.

Q.13 What should be the measure of the angle between slide 2 and ground if the length of AB is 1.2√3 m?

1. 30°
2. 45°
3. 60°
4. 90°

Answer. (3)

Q.14 If slide 1 makes an angle of 150° with the flat part and FD = 8.5 m, what is the height of the top point of slide 1 from the ground (EC)?

1. 5 m
2. 8.6 m
3. 10 m
4. 12.1 m

Answer. (2)

Q.15 What should be the length of slide 2 if the angle between slide 2 and ground is 30°?

1. 4.24 m
2. 5.04 m
3. 6.12 m
4. 7.2 m

Answer. (4)

👉 Read Also- CBSE Class 10 Half-Yearly/Mid Term 2024-25 : Most Important Questions with Answers; PDF Download (All Subjects)

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