# NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.3

Mathematics is a highly conceptual subject that requires a considerable amount of practice. In order to achieve good grades in the subject, students must have a clear understanding of the basics of the curriculum. Mathematics is not only a fundamental academic discipline but also the foundation for many scientific theories and concepts, which are indispensable to many other disciplines. Class 10 Mathematics introduces students to a wide range of concepts, therefore, it is challenging for them to have a good command of all the concepts of the subject’s curriculum. Good scores in Mathematics are primarily determined by the amount of practise students put in. In order to have a thorough understanding of Chapter-8 Introduction to Trigonometry, Extramarks provides students with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3. Practising the questions provided in the NCERT textbook consistently is the first step to building strong fundamentals in Mathematics. To help students achieve their academic goals and attain success in the Class 10 board examinations, Extramarks provides students with NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3.

## CBSE Class 10 NCERT Solutions for Maths Chapter 8 – Introduction to Trigonometry

Class 10 represents a critical point in a student’s academic career. Choosing the subjects for higher studies is an important decision. In a way, this academic session structures the careers of students. They also learn the basic concepts of every subject in this academic session, therefore, they should be very careful with their academic performance in Class 10. These scores determine the future trajectory of students. Furthermore, the scores of Class 10 are also evaluated at the time of awarding various academic scholarships. Extramarks is an e-learning platform that has taken the initiative to provide students with all the resources they need to have a successful academic career. Therefore, the learning website provides them with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3.

## Access NCERT Solutions for class 10 Maths Chapter 8 – Introduction to Trigonometry

The subject of Mathematics can be intimidating for many students. To prepare for the Class 10 Mathematics board examination, students must thoroughly review the NCERT curriculum. However, the NCERT textbooks do not include solutions to the questions incorporated in them. Therefore, Extramarks provides students with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 in order to assist them in preparing for their examinations. These Extramarks solutions walk students through every step of the solution and help them understand the logic and concept behind it.By practising NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.3, students can solve problems more accurately and efficiently.

This helps them  perform considerably better in their board examinations. Furthermore, the learning portal also provides them with NCERT Solutions for all the chapters of Class 10 Mathematics. Extramarks provides students with easy access to the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3. Students need to practise Mathematics regularly in order to improve their conceptual clarity. One of the best resources for preparing for the board examinations are the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 provided by Extramarks. There would be an increase in the speed and accuracy with which students solve mathematical problems. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 can be easily accessed at one’s own convenience as they are available in PDF format.

## NCERT Solution Of Maths Class 10 Chapter 8 Exercise 8.3 – Free PDF Download

The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 provided by Extramarks are designed in collaboration with specialised educators. Using the Extramarks website, students have access to accurate and detailed study material that is convenient and authentic. Extramarks suggests that learners download the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 from the Extramarks website so that they can comprehend the concepts of the chapter and then practise them thoroughly. Students can solve all the difficult problems in Chapter 8 Introduction to Trigonometry with precision and speed when they have a steady pace and a concrete understanding of concepts, which they can attain with the help of these solutions. Extramarks’ NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 makes it easy for students to understand the complicated operations, identities, and concepts of the chapter. Extramarks provides students with expert solutions and Live Doubt-Solving Sessions so that students can resolve all their doubts and learn effectively to perform well in their board examinations. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 provided by Extramarks are extremely useful for quick revisions, as they are simplified answers compiled in an easy-to-understand language. If the solutions are not presented in a logical manner, students may find it difficult to clear their doubts. Students can also earn marks based on step-by-step marking in Mathematics. Accordingly, Extramarks provides students with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 which are properly detailed step-by-step solutions.

### NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.3: History of Trigonometry

Students can join the Extramarks website for access to convenient and trustworthy study material. There are numerous significant properties and identities in the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3. For the students to succeed in the board examinations, it is imperative that they acquire familiarity with these operations and concepts. . Students can refer to the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 in order to comprehend this chapter’s complex concepts and operations. Extramarks is a platform that aims to promote the holistic development of students. It offers learners comprehensive study material so that they can learn, practise and excel in their academic careers. NCERT books aid in forming the knowledge base of students, therefore, Extramarks offers students NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 to assist with this task. Students can also refer to the learning website for access to the NCERT Solutions Class 12, NCERT Solutions Class 11, NCERT Solutions Class 10, NCERT Solutions Class 9, NCERT Solutions Class 7, NCERT Solutions Class 8, NCERT Solutions Class 6, NCERT Solutions Class 4, NCERT Solutions Class 3, NCERT Solutions Class 5, NCERT Solutions Class 1, NCERT Solutions Class 2 and various other reliable learning resources.

### Important Topics under NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.3

The Class 10th Maths Chapter 8 Exercise 8.3 is based on the concept of Trigonometric Ratios of Complementary Angles. Students can find it challenging to comprehend the logical rationale behind the solutions to this concept. Introduction to Trigonometry is one of the most complicated chapters of the curriculum of Class 10, therefore students should be very careful when going through the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3. In order to succeed in Class 10, students should have a holistic understanding of the NCERT curriculum. This is the first step in building their fundamentals and clarifying their basic concepts. It is essential that students have access to credible solutions to NCERT questions in order to avoid confusion while searching for them. Therefore, Extramarks provides learners with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 so that they can get reliable and accurate solutions without having to look anywhere else.

### Importance of Trigonometry in Mathematics

The study of Trigonometry is concerned with the relationship between angles, lengths, and heights. During the third century, it was utilised in a variety of fields, including Astronomy and Geometric studies. Now, it is being used in a wide range of fields, including Engineering, Physics, Architecture, Astronomy, Survey, and even crime scene investigation. Students can refer to the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 provided by Extramarks for a better understanding of the theme of Trigonometry. Besides Astronomy and Geography, Trigonometry can also be applied to Computer Music, Chemistry Number Theory, Medical Imaging, Electronics, Electrical Engineering, Civil Engineering, Satellite Navigation, Architecture, Mechanical Engineering, Oceanography, Seismology, Phonetics, Image Compression, and Game Development, among other fields. Students can learn how to apply trigonometric concepts in real life by practising the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 provided by Extramarks.

### Class 10 Maths Exercise 8.3: What is it All About

A Trigonometric calculation involves the use of triangles in the study of lengths, heights, and angles. In daily life, trigonometry and its functions have a wide range of applications. It is used in Geography to measure distances between landmarks, in Astronomy to measure distances between nearby stars, as well as in Satellite Navigation. Therefore, students should have a thorough understanding of the  NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 provided by Extramarks.

### CBSE Class 10 Maths Chapter 8 Exercise 8.3 Solutions: Important Considerations

Chapter 8 Class 10 Mathematics contains overall four exercises. The chapter introduces students to several topics such as Trigonometric Ratios, Trigonometric Ratios of Some Specific Angles, Trigonometric Ratios of Complementary Angles and Trigonometric Identities. The Class 10 Maths Chapter 8 Exercise 8.3 is based on the concept of Trigonometric Ratios of Complementary Angles. The exercise contains five questions which include several parts. Students can find the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 a bit difficult in the beginning as the chapter contains many complicated concepts which can be challenging for the students. However, these solutions are crafted in very simple and straightforward language so that learners do not face any difficulty when going through them. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 are one of the best resources for the preparation for the Class 10 Mathematics board examination.

### NCERT Solution of Maths Class 10 Chapter 8 Exercise 8.3: Solved Examples

Chapter 8 Introduction to Trigonometry is a prominent theme in the Class 10 Mathematics curriculum which requires a great deal of practise as it includes a variety of new concepts that could be challenging for students to understand. Therefore, to facilitate the learning process and the preparation of students, Extramarks provides them with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3. Despite that, just going through these NCERT Solutions is not enough for students to build a strong grasp of these concepts, as NCERT Textbooks contain a limited number of questions. Therefore, along with NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3, students should also go through various exemplar questions and extra questions so that they can have a clear and strong comprehension of the concepts of the chapter.

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### NCERT Solutions for Class 10 Maths

Mathematics is one of the most important subjects in the academic career of students. To score well in this subject, students must practise meticulously. Moreover, since Mathematics is a conceptual subject, students should have a sound understanding of the subject in order to perform well in the Class 10 board examinations. Chapter 8 of Class 10 Mathematics Introduction to Trigonometry presents a number of challenges to students. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 are a vital resource for them to grasp the concepts of Chapter 8 Trigonometry.  These solutions would assist learners with a consistent learning experience. Extramarks strives to assist students in achieving higher scores in their board examinations by providing them with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3.

### Access Other Exercises of Class 10 Maths Chapter 8

It is important for students to practice the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 thoroughly in order to be able to solve any question related to the designated chapter easily. Extramarks provides students with complete and convenient study material so that they can achieve their academic goals and stand out in any examinations. The NCERT textbooks cover the entire syllabus of the subject, so it is essential that students have access to NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 in order to achieve the highest possible grades in the board examinations. As NCERT books are written by highly qualified subject experts, students will be able to grasp all the concepts of the chapter if they thoroughly review the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3. These solutions make students ready for their board examinations and maintain their confidence so that they can excel in their examinations. Along with the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3, the solutions to all the other exercises in the chapter are available on Extramarks.

Q.1

$\begin{array}{l}\text{Evaluate\hspace{0.17em}:}\\ \text{(i)}\frac{\text{sin 18°}}{\text{cos 72}°}\text{}\\ \text{(ii)}\frac{\text{tan 26°}}{\text{cot 64°}}\text{}\\ \text{(iii) cos 48°}-\text{sin 42°}\\ \text{(iv) cosec 31°}-\text{sec 59°}\end{array}$

Ans

$\begin{array}{l}\text{(i)}\\ \text{}\frac{\text{sin 18°}}{\text{cos 72}\mathrm{°}}=\frac{\text{cos(90°}-18\text{°}\right)}{\text{cos 72}\mathrm{°}}=\frac{\text{cos 72}\mathrm{°}}{\text{cos 72}\mathrm{°}}=1\\ \\ \text{(ii)}\\ \text{}\frac{\text{tan 26°}}{\text{cot 64°}}=\frac{\text{cot (90°}-\text{26°)}}{\text{cot 64°}}=\frac{\text{cot 64°}}{\text{cot 64°}}=1\\ \\ \text{(iii)}\\ \text{cos 48°}-\text{sin 42°}=\text{sin (90°}-\text{48°)}-\text{sin 42°}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\text{sin 42°}-\text{sin 42°}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=0\\ \text{(iv)}\\ \text{cosec 31°}-\text{sec 59°}=\text{sec (90°}-\text{31°)}-\text{sec 59°}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\text{sec 59°}-\text{sec 59°}\\ \text{\hspace{0.17em}\hspace{0.17em}}=0\end{array}$

Q.2

$\begin{array}{l}\text{Show that\hspace{0.17em}:}\\ \text{(i) tan 48° tan 23° tan 42° tan 67°}=1\\ \text{(ii) cos 38° cos 52°}-\text{sin 38° sin 52°}=0\end{array}$

Ans

$\begin{array}{l}\text{(i)}\\ \text{tan 48° tan 23° tan 42° tan 67°}\\ =\text{cot (90°}-\text{48°) cot (90°}-23\text{°) tan 42° tan 67°}\\ =\text{cot}42°\text{\hspace{0.17em} cot 67°\hspace{0.17em}\hspace{0.17em}tan 42°\hspace{0.17em}\hspace{0.17em}tan 67°}\\ =\text{cot}42°\text{\hspace{0.17em}tan 42°\hspace{0.17em}\hspace{0.17em}tan 67° cot 67°}\\ =1×1=1\\ \text{(ii)}\\ \text{cos 38° cos 52°}-\text{sin 38° sin 52°}\\ =\mathrm{sin}\text{(90°}-3\text{8°)\hspace{0.17em}cos (90°}-3\text{8°)}-\text{sin 38° sin 52°}\\ =\mathrm{sin}\text{\hspace{0.17em}\hspace{0.17em}52°\hspace{0.17em}}\mathrm{sin}38\text{°}-\text{sin 38° sin 52°}\\ =0\end{array}$

Q.3

$\text{If tan 2A}=\text{cot}\left(\text{A}-18\mathrm{°}\right),\text{where 2A is an acute angle},\text{find the value of A}.$

Ans

$\begin{array}{l}\text{Given that,}\\ \text{tan 2A}=\text{cot}\left(\text{A}-18\mathrm{°}\right)\\ \text{or cot (90°}-2\text{A}\right)=\text{cot}\left(\text{A}-18\mathrm{°}\right)\\ \text{or 90°}-2\text{A}=\text{A}-18\mathrm{°}\\ \text{or}3\text{A}=108\mathrm{°}\\ \text{or A}=\frac{108\mathrm{°}}{3}=36\mathrm{°}\end{array}$

Q.4

$\text{If tan A}=\text{cot B, prove that A}+\text{B}=\text{90°.}$

Ans

$\begin{array}{l}\text{Given that,}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} tan A}=\text{cot B}\\ \text{or cot (90°}-\text{A)}=\mathrm{cot}\text{\hspace{0.17em}\hspace{0.17em}B}\\ \text{or 90°}-\text{A}=\text{B}\\ \text{or A}+\text{B}=\text{90°}\end{array}$

Q.5

$\text{If sec 4A}=\text{cosec (A}-\text{20°), where 4A is an acute angle, find the value of A.}$

Ans

$\begin{array}{l}\text{Given that,}\\ \text{sec 4A}=\text{cosec (A}-\text{20°)}\\ \text{or cosec (90°}-\text{4A)}=\text{cosec (A}-\text{20°)}\\ \text{or 90°}-\text{4A}=\text{A}-\text{20°}\\ \text{or 5A}=110\text{°}\\ \text{or A}=\frac{110\text{°}}{5}=22\text{°}\end{array}$

Q.6

$\begin{array}{l}\text{If A, B and C are interior angles of a triangle ABC,}\\ \text{then show that}\\ \text{sin}\left(\frac{\text{B+C}}{2}\right)=\mathrm{cos}\frac{\text{A}}{2}.\end{array}$

Ans

$\begin{array}{l}\text{Given that A, B and C are interior angles of a triangle ABC.}\\ \therefore \text{A}+\text{B}+\text{C}=180\mathrm{°}\\ \text{or A}=180\mathrm{°}-\text{B}-\text{C}\\ \text{Now,}\\ \text{sin}\left(\frac{\text{B}+\text{C}}{2}\right)=\mathrm{cos}\left(90\mathrm{°}-\frac{\text{B}+\text{C}}{2}\right)\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\mathrm{cos}\left(\frac{180\mathrm{°}-\text{B}-\text{C}}{2}\right)\\ \text{}=\mathrm{cos}\left(\frac{\text{A}}{2}\right)\text{}\end{array}$

Q.7

$\text{Express sin 67°}+\text{cos 75° in terms of trigonometric ratios of angles between 0° and 45°.}$

Ans

$\begin{array}{l}\text{sin 67°}+\text{cos 75°}=\mathrm{cos}\text{(90°}-\text{67°)}+\text{sin (90°}-\text{75°)}\\ \text{}=\mathrm{cos}23\text{°}+\text{sin 15°}\end{array}$

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### 1. Are the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 difficult?

No, the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 provided by the Extramarks website are not difficult for students. These solutions are produced by the subject specialists of Mathematics of Extramarks in a very easy-to-understand and straightforward language. These solutions are well-structured and explained in a step-by-step manner so that students can easily understand the logic behind the concepts of the chapter.

### 2. Is it necessary to practice all the questions of the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3?

Yes, students should practice all the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3 as these solutions assist them in strengthening their fundamentals of the subject’s curriculum. Furthermore, practising them provides learners with a steady pace and increases their efficiency. Every question of the exercise contains a new concept and also practising these solutions help students in preventing the small calculation errors that might occur while solving the problems of the chapter.

### 3. How can students clear their doubts about the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.3?

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