NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2
NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 provide step-by-step explanations for solving trigonometric problems. These solutions help students understand the application of trigonometric ratios in real-life situations, enhancing problem-solving skills and boosting exam preparation.
Ananya Gupta8 Jan, 2025
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NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2: The NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 focus on applying trigonometric ratios to solve problems related to right-angled triangles. This exercise requires students to find the values of sine, cosine, tangent, and other trigonometric functions for given angles.
By practicing these problems, students will strengthen their understanding of how trigonometric ratios are used in various practical scenarios. These solutions provide clear explanations and step-by-step methods to help students grasp the concepts effectively and build confidence in solving trigonometric problems.NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 Overview
NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 focuses on applying the concepts of trigonometric ratios to solve problems involving right-angled triangles. This exercise involves using the basic trigonometric ratios sine, cosine, tangent, cosecant, secant, and cotangent to find the unknown sides or angles of a right-angled triangle when certain information is provided. The solutions guide students step-by-step to arrive at the correct answers, providing clear explanations and methods for finding the missing sides or angles. This exercise is essential for building a strong foundation in trigonometry.NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 PDF
The NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 provide detailed step-by-step solutions to the questions in the exercise. These solutions will help students understand how to apply trigonometric ratios in various problems involving right-angled triangles. You can access the PDF of the solutions below to aid your preparation and improve your understanding of trigonometry.NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 PDF
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2
Below is the NCERT Solutions for Class 10 Maths Chapter 8 - Introduction to Trigonometry Exercise 8.2Solve the followings Questions.
1. Evaluate the following : (i) sin 60° cos 30° + sin 30° cos 60° (ii) 2 tan 2 45° + cos 2 30° – sin 2 60° (iii) cos 45°/(sec 30° + cosec 30°) (iv) (sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°) (v) (5cos 2 60° + 4sec 2 30° - tan 2 45°)/(sin 2 30° + cos 2 30°)Answer:
(i) sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan
2
45° + cos
2
30° – sin
2
60°
(iii) cos 45°/(sec 30° + cosec 30°)
(iv) (sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)
(v) (5cos
2
60° + 4sec
2
30° - tan
2
45°)/(sin
2
30° + cos
2
30°)
2. Choose the correct option and justify your choice :
(i) 2tan 30°/1+tan
2
30° =
(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°
(ii) 1-tan
2
45°/1+tan
2
45° =
(A) tan 90° (B) 1 (C) sin 45° (D) 0
(iii) sin
2
A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°
(iv) 2tan30°/1-tan
2
30° =
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°
Answer:
(i) 2tan 30°/1+tan 2 30° = (A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30° =
(ii) 1-tan
2
45°/1+tan
2
45° =
(A) tan 90° (B) 1 (C) sin 45° (D) 0
(iii) sin
2
A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°
(iv) 2tan30°/1-tan
2
30° =
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°
3. If tan (A + B) = √3 and tan (A – B) = 1/√3; 0° < A + B ≤ 90°; A > B, find A and B.
Answer:
……….(i)
4. State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.
Answer:
(i) False. Let A = 30° and B = 60°, then sin (A + B) = sin (30° + 60°) = sin 90° = 1 and, sin A + sin B = sin 30° + sin 60° = 1/2 + √3/2 = 1+√3/2 (ii) True. sin 0° = 0 sin 30° = 1/2 sin 45° = 1/√2 sin 60° = √3/2 sin 90° = 1 Thus the value of sin θ increases as θ increases. (iii) False. cos 0° = 1 cos 30° = √3/2 cos 45° = 1/√2 cos 60° = 1/2 cos 90° = 0 Thus the value of cos θ decreases as θ increases. (iv) True. cot A = cos A/sin A cot 0° = cos 0°/sin 0° = 1/0 = undefined.Benefits of Solving NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2
Concept Clarity : By solving the exercise, students reinforce their understanding of trigonometric ratios and their application to right-angled triangles. Improved Problem-Solving Skills : The solutions guide students through each step, helping them develop a systematic approach to solving problems and improving their problem-solving skills. Boost Confidence : Regular practice with detailed solutions boosts students' confidence in tackling different types of trigonometry problems during exams. Mastering Trigonometric Ratios : Exercise 8.2 focuses on applying trigonometric ratios in real-life contexts, helping students master the use of these ratios in various mathematical problems. Better Exam Preparation : As the exercise includes a wide range of questions, it helps students prepare thoroughly for exams and improves their accuracy and speed. Clear Understanding of Formulas : The exercise aids in memorizing key trigonometric formulas by applying them repeatedly in different contexts, leading to better retention.NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 FAQs
How do I apply the trigonometric ratios in this exercise?
To solve problems in Exercise 8.2, identify the right-angle triangle and the relevant sides (opposite, adjacent, or hypotenuse). Then, apply the appropriate trigonometric ratio (sine, cosine, or tangent) to find the unknown values.
Are the solutions for Exercise 8.2 available?
Yes, the NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2 are available and provide step-by-step explanations for all the problems in the exercise.
What are the benefits of solving Exercise 8.2?
Solving this exercise helps students:
Strengthen their understanding of trigonometric ratios.
Improve their ability to apply trigonometric concepts in real-world problems.
Build confidence in solving complex problems involving heights, distances, and angles.
How can I improve my accuracy in solving Exercise 8.2?
To improve accuracy:
Practice regularly to understand the trigonometric ratios and how to apply them.
Focus on drawing clear diagrams of the triangles.
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