NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.4

The system of school education in India is overseen and managed by the Central Board of Secondary Education, situated in New Delhi. CBSE ensures the smooth functioning of a national education system. The National Council of Educational Research and Training was established in 1961 with the goal of improving the quality of school education in India. This organisation provides advisory and assistance services to state and federal governments. It also creates and publishes educational kits, instructional manuals, textbooks, supplementary materials, newsletters, journals, and multimedia products.

Class 10 is an integral part of a student’s educational career. Their future is determined by the marks obtained in the board examinations. Students can choose from Humanities, Commerce, or Science streams based on their marks and interests. There is no doubt that the subject of Mathematics can be challenging, but it can also be rewarding. Mathematical concepts of Class 10 are not difficult to learn when practised properly and with full concentration. Students must achieve a minimum score of 33% on both the theory and practical examinations in order to be promoted to Class 11 and subsequently to Class 12.

Trigonometry is based on the concept of triangles and Pythagoras’s theorem. The mathematical concept referred to as Trigonometry can be used to determine distances or heights using some mathematical techniques. ‘Trigonometry’ is derived from a combination of three ancient Greek terms, ‘tri’ for three, ‘gon’ for sides, and ‘metron’ for measurement. The study of trigonometry deals with the relationship between a triangle’s sides and angles. Trigonometric concepts continue to be used in the most technologically advanced Engineering and Physical Science disciplines today. The purpose of this chapter is to study some trigonometric ratios of acute angles with respect to the sides of a right triangle.

To prepare well for  Class 10 Chapter 8 Introduction to Trigonometry, students should take assistance from the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 available on the Extramarks website. Exercise 8.4 Class 10 Maths NCERT Solutions can assist students in improving their mathematical abilities, as well as their logical and arithmetic skills. Solutions to difficult problems are explained in a simplified manner in order to facilitate learning. Practising textbook solutions is essential for students preparing for the Class 10 Mathematics examination.

The objective of the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 is to provide students with answers to all questions from the textbook in order to assist them in understanding the questions better. There are numerous competitive examinations, as well as college entrance tests, that are based on the content encapsulated in the NCERT textbooks. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 should be regularly practised by students in order to achieve higher test scores. Students are able to gain a deeper understanding of the importance of studying Class 10 Mathematics with the assistance of these solutions. Several study materials are available on the Extramarks website to help them become familiar with the concepts discussed in this chapter.

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry (Ex 8.4) Exercise 8.4

The Extramarks website makes it considerably convenient to find the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. Students should pay special attention to the questions in Class 10 Maths Chapter 8 Exercise 8.4 in preparation for the final Mathematics Class 10 board examination since it is one of the most important chapters. Students can access a variety of study materials through the Extramarks website and mobile application. They can find a variety of resources to help them prepare for the examinations on the website, such as past years’ papers, revision notes, sample papers, and extra questions. Learners can use the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 available on Extramarks, to prepare for their examinations.

In order to assist students with their studies, a panel of experts prepares solutions based on the most recent Class 10 CBSE syllabus. Students can use the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 to help them understand the questions. They are given both solutions and explanations to help them understand the concepts used in the questions. Students can access the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 at any time and from any location to prepare for the Class 10 board examination. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 can be downloaded from Extramarks in PDF format in order for students to score well.

Access NCERT Solutions for Class 8 Maths Chapter 8 – Introduction to Trigonometry 

In Mathematics, Trigonometry is the study of the relationship between triangle sides and angles, as well as all functions that are related to angles. Class 10 Mathematics covers the topic of Trigonometry. In addition to enhancing students’ understanding of some of the most important concepts, it also helps them develop their problem-solving skills. The use of this technology is widespread in daily life. Therefore, students are encouraged to learn as much as possible about the topics discussed in Introduction to Trigonometry. There is a complete set of questions and study materials available on Extramarks to assist students with their preparation for the Class 10 Maths Exercise 8.4.

Refer to Page 1 – 22 for Exercise 8.4

For answers to questions in the Class 10 Mathematics textbook, students should consult the NCERT Solutions for Class 10 Maths, Chapter 8, Exercise 8.4.It is important for students to be able to comprehend all the concepts discussed in this chapter. Since NCERT books contain questions which frequently occur in examinations, it is generally beneficial to practise exercises from them. This chapter contains a number of questions that students may find difficult to answer. Extramarks provides the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. Students are advised to prepare for the examination by using authentic and reliable solutions. Through the Extramarks learning platform, students can access study materials, such as NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4.

CBSE Class 10 Maths Chapter 8 Exercise 8.4 Solutions Free PDF

These NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 can be used by students to accelerate their learning and improve their academic performance. As a result of these solutions, they are better able to understand the problems.In order to improve students’ understanding of concepts, Extramarks provides students with the opportunity to practise solving practise modules. For students preparing for examinations or working on homework assignments, NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 is an excellent resource. The ability to understand concepts and numerical problems is essential for passing the Class 10 board exams. It is strongly advised that students use the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 to prepare for board exams.

Class 10 Maths Exercise 8.4 Solutions 

For Class 10 Mathematics Chapter 8 Exercise 8.4, NCERT Solutions provide detailed explanations for all questions to facilitate concept-based learning. The simple language used in the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 facilitates easier retention and understanding of the questions. Besides the practise questions provided for each subject, students are also encouraged to answer additional practise questions to track their progress. Extramarks provides detailed solutions prepared by subject matter specialists in accordance with the syllabus and examination format. Extramarks offers chapter-by-chapter solutions to all Class 10 subjects. Students can review the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 available in PDF format on the Extramarks website. Effective examination preparation necessitates a thorough review of the material prior to the examination.

Exercise 8.4 Class 10 Question 1 

Students are asked to express the trigonometric ratios sin, sec, and tan in terms of cot of an angle in the first question of Class 10 Mathematics experiment 8.4. In order to answer this question, students need to make use of certain trigonometric identities.

Exercise 8.4 Class 10 Question 2 

In the second question of this exercise, they are required to determine all the trigonometric ratios of an angle θ in terms of Sec θ.

Exercise 8.4 Class 10 Question 3 

Class 10 Mathematics Trigonometry Exercise 8.4 question 3 consists of two parts in which students need to calculate the value of an evidently complex trigonometric function involving different angles. In order to find the values of the two trigonometric equations, students can use various concepts learned in Trigonometry, such as trigonometric identities and formulas.

Exercise 8.4 Class 10 Question 4 

There are four subparts to the fourth question of Trigonometry Class 10 Exercise 8.4. Several trigonometric equations are presented, and the values of these equations must be selected from four options. Besides selecting the correct answer, students must also explain why they selected that particular answer. Many trigonometric identities are used in the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 provided by Extramarks.

Exercise 8.4 Class 10 Question 5 

For Class 10 Mathematics Chapter 8 Exercise 8.4 Question 5, students are required to prove ten trigonometric identities. Students must apply trigonometric relationships to solve the angles for each of those ten identities.

Key Features of NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.4 

Students can study the entire chapter, exercise-wise at their own pace using the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. Students can gain a better understanding of the importance of studying Class 10 Mathematics Chapter 8 Exercise 8.4 by practising with the aid of NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. The Trigonometry Class 10 Exercise 8.4 Solutions can be used to prepare for a wide range of competitive examinations. Extramarks offers a variety of study materials to help students gain a deeper understanding of the concepts presented in this chapter. The study materials also include the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 and all the key concepts outlined in the CBSE-recommended syllabus.

The solutions, created by highly qualified mentors, are meant to help students better prepare for board exams. In addition to competitive examinations, the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 can be used to study for various entrance examinations. Students should practise the questions in the NCERT Textbook for Class 10 Mathematics Chapter 8 Exercise 8.4 at least twice before the Class 10 board examination. NCERT Solutions for each chapter are readily available to assist students in gaining a thorough understanding of the subject. Subject experts created the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 with the comprehension abilities of Class 10 students in mind. This makes them easier for students to understand.

The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 offer the following advantages:

  • Following the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 allows students to clarify their doubts at a deeper level, enabling them to attempt similar problems independently.
  • Answers to all Class 10 Chapter 8 NCERT Textbook questions are included in the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4.
  • In order to provide students with high-quality NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4, the instructors of Extramarks strictly adhered to the guidelines provided by CBSE.
  • In order to facilitate quick revision, it is extremely convenient to have the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 accessible in PDF format.

NCERT Solutions for Class 10 Maths Chapter 8 Exercises 

Using NCERT textbooks and solutions, students can gain a comprehensive understanding of each concept. Students can understand all concepts covered in them, including advanced concepts, by using these NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. Extramarks makes it simple for students to find the NCERT Solutions For Class 10 Mathematics Chapter 8. These NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 are intended to meet the needs of students who are striving for academic excellence. Exercise 8.4 Class 10 Maths NCERT Solutions are useful because they are written in an easy-to-understand style.

One of the most significant benefits of these NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4  is that they can be downloaded online andused offline. This feature is especially beneficial for students who do not have constant internet access while preparing for examinations. Thus, they can download the NCERT Solutions For Class 10 Chapter 8 Exercise 8.4 available in PDF format. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 can be used to revise for finals and prepare for examinations. The NCERT Solutions For Class 10 Chapter 8 Exercise 8.4 cover all the topics covered in the CBSE Class 10 Mathematics Syllabus.

Students are explained all major concepts, terminologies, questions, and formulas so that they fully comprehend the material. Students can use the Trigonometry Class 10 Exercise 8.4 Solutions to improve their performance in competitive examinations, aptitude tests, and college entrance examinations. Extramarks provides the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 to help students gain a thorough understanding of the concepts. The problems in Class 10 NCERT Solutions are explained in detail. The Extramarks website offers students revision notes, sample papers, past years’ papers, assignments, additional questions, worksheets, and, most importantly, NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 to help them prepare for the board exams.

Q.1 

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

Ans

We know that cosec2 A=1+cot2 Aor    1sin2A=1+cot2 Aor   sin2A=11+cot2 Aor  sinA=11+cot2 AAlso, we know that sec2 A=1+tan2 Aor sec2 A=1+1cot2 Aor sec A=1+cot2Acot2A=1+cot2AcotAAlso, we know that tan A=sinAcosA=1cosAsinA=1cotA

Q.2 

Write all the other trigonometric ratios of ∠A in terms of sec A.

Ans

We know that sin2 A=1−cos2 Aor   sin2 A=1−1sec2 Aor   sin2A=sec2 A−1sec2 Aor  sinA=sec2 A−1sec Aor 1cosec A=sec2 A−1sec Aor cosec A=sec Asec2 A−1Also, we know that sec A cos A=1or cos A=1sec AAlso, we know that sec2A−tan2 A=1or tan2 A=sec2A−1or tan A=sec2A−1Also, we know that tan A cot A=1or cot A=1tan A=1sec2A−1

Q.3

Evaluate: (i) sin2 63°+sin2 27°cos2 17° +cos2 73° (ii) sin 25° cos 65°+cos 25° sin 65°

Ans

(i) sin2 63°+sin2 27°cos2 17° +cos2 73°=sin2 63°+cos2(90°−27°)sin2(90°−17°)+cos2 73°    =sin2 63°+cos2 63°sin2 73°+cos2 73°                                               =11=1(ii) sin 25° cos 65°+cos 25° sin 65°=sin 25° sin(90°−65°)+cos 25° cos(90°− 65°)=sin 25° sin 25°+cos 25° cos 25°=sin2 25°+cos225°=1

Q.4

Choose the correct option. Justify your choice.(i) 9 sec2A−9 tan2A= (A) 1 (B) 9 (C) 8 (D) 0(ii) (1 + tan θ+ sec θ) (1 + cotθ−cosecθ)= (A) 0 (B) 1 (C) 2 (D) −1(iii) (sec A + tan A) (1−sin A) = (A) sec A (B) sin A (C) cosec A (D) cos A(iv) 1+tan2A1+cot2 A= (A) sec2A (B) −1 (C) cot2A (D) tan2A

Ans

(i) 9 sec2A−9 tan2A=9(sec2A−tan2A)=9×1=9Therefore, the correct option is (B).(ii) (1+tanθ+sec θ) (1+cotθ−cosec θ)=(1+sinθcosθ+1cosθ)(1+cosθsinθ−1sinθ)=(sinθ+cosθ+1cosθ)(sinθ+cosθ−1sinθ)=(sinθ+cosθ)2−1sinθcosθ=sin2θ+cos2θ+2sinθcosθ−1sinθcosθ=1+2sinθcosθ−1sinθcosθ=2Therefore, the correct option is (C).(iii) (sec A + tan A) (1−sin A)=(1cos A+sinAcos A)(1−sin A)=(1+sinAcos A)(1−sin A)=1−sin2Acos A=cos2Acos A=cosATherefore, the correct option is (D).(iv)    1+tan2A1+cot2A=sec2Acosec2A=sin2Acos2A=tan2ATherefore, the correct option is (D).

Q.5

Prove the following identities, where the angles involvedare acute angles for which the expressions are defined.(i) (cosecθ−cotθ)2=1−cosθ1+cosθ(ii) cosA1+sinA+1+sinAcosA=2secA(iii) tanθ1−cotθ+cotθ1−tanθ=1+secθcosecθ [Hint :Write the expression in terms of sinθ and cosθ.](iv) 1+secAsecA=sin2A1−cosA [Hint: Simplify LHS and RHS separately](v) cosA−sinA+1cosA+sinA−1=cosec A+cot A, using the identity cosec2A=1+cot2 A.(vi) 1+sinA1−sinA=secA+tanA(vii) sinθ−2sin3θ2cos3θ−cosθ=tanθ(viii) (sin A + cosec A)2+(cos A+sec A)2=7+tan2A+cot2A(ix) (cosec A−sin A) (sec A−cos A)=1tanA+cotA [Hint: Simplify LHS and RHS separately](x) 1+tan2A1+cot2A=(1−tanA1−cot A)2=tan2A

Ans

(i) LHS=(cosecθ−cotθ)2         =cosec2θ+cot2θ−2cosecθ cotθ         =1sin2θ+cos2θsin2θ−2cosθsin2θ         =1+cos2θ−2cosθsin2θ         =(1−cosθ)(1−cosθ)1−cos2θ=(1−cosθ)(1−cosθ)(1+cosθ)(1−cosθ)        =1−cosθ1+cosθ=RHS(ii) LHS=cosA1+sinA+1+sinAcosA =cos2A+(1+sinA)2(1+sinA)cosA =cos2A+sin2A+2sinA+1(1+sinA)cosA        =1+1+2sinA(1+sinA)cosA =2(1+sinA)(1+sinA)cosA=2secA=RHS (iii) LHS=tanθ1−cotθ+cotθ1−tanθ                 =sinθcosθ1−cosθsinθ+cosθsinθ1−sinθcosθ         =sinθcosθsinθ−cosθsinθ+cosθsinθcosθ−sinθcosθ         =sin2θcosθ(sinθ−cosθ)+cos2θsinθ(cosθ−sinθ)        =sin3θ−cos3θsinθcosθ(sinθ−cosθ)      =(sin2θ+cos2θ+sinθcosθ)(sinθ−cosθ)sinθcosθ(sinθ−cosθ) =1+sinθcosθsinθcosθ=1+secθcosec θ=RHS(iv)LHS=1+secAsecA=1+1cosA1cosA=1+cosA1×1−cosA1−cosA =1−cos2A1−cosA=sin2A1−cosA=RHS(v) LHS=cosA−sinA+1cosA+sinA−1         =cosAsinA−sinAsinA+1sinAcosAsinA+sinAsinA−1sinA         =cotA−1+cosecAcotA+1−cosec A         =cotA−(1−cosecA)cotA+(1−cosec A)×cotA−(1−cosec A)cotA−(1−cosec A)         =cot2A+(1−cosecA)2−2cotA(1−cosec A)cot2A−(1−cosec A)2         =cot2A+1+cosec2A−2cosecA−2cotA+2cotAcosecAcot2A−1−cosec2 A+2cosec A    =2cosec2A−2cosecA−2cotA+2cotAcosecA−1−1+2cosec A         =cosecA(cosecA−1)+cotA(cosec A−1)cosec A−1    =cosecA+cot A(vi)LHS=1+sinA1−sinA=1+sinA1−sinA×1+sinA1+sinA =(1+sinA)11−sin2A=1+sinAcosA=tanA+secA=RHS(vii) LHS=sinθ−2sin3θ2cos3θ−cosθ         =sinθ(1−2sin2θ)cosθ(2cos2θ−1)         =sinθ(1−2sin2θ)cosθ(2(1−sin2θ)−1)         =sinθ(1−2sin2θ)cosθ(2−2sin2θ−1)         =sinθ(1−2sin2θ)cosθ(1−2sin2θ)         =tanθ=RHS(viii) LHS=(sin A+cosec A)2+(cos A+sec A)2   =sin2A+cosec2A+2+cos2A+sec2A+2 =sin2A+cos2A+4+sec2A+cosec2A =1+4+1+tan2A+1+cot2A         =7+tan2A+cot2A=RHS(ix) LHS=(cosec A−sin A) (sec A−cos A)         =(1sinA−sinA)(1cosA−cosA)         =(1−sin2AsinA)(1−cos2AcosA)         =cos2AsinA×sin2AcosA=sinAcosA1=sinAcosAsin2A+cos2A         =1sin2A+cos2AsinAcosA=1sinAcosA+cosAsinA        =1tanA+cotA        =RHS(x) LHS=1+tan2A1+cot2A=sec2Acosec2A=1cos2A1sin2A=sin2Acos2A=tan2A=RHSLHS=(1−tanA1−cot A)2=(1−sinAcosA1−cosAsinA)2=(cosA−sinAcosAsinA−cosAsinA)2         =sin2Acos2A=tan2A=RHS

Please register to view this section

FAQs (Frequently Asked Questions)

1. How can NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 assist students in understanding important concepts?

Since all solutions are written in a straightforward and easy-to-understand language, students can greatly benefit from the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. Practising examples and NCERT solutions can assist students in gaining a better understanding of Mathematical concepts and achieving high exam scores. Students benefit from Extramarks’ NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 by gaining a thorough understanding of the fundamentals and being able to comprehend concepts more effectively. Students can access these solutions via the Extramarks website and mobile application.

2. What are the advantages of using the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4?

Those students in Class 10 who are studying Mathematics Chapter 8 may benefit from the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. Students are given answers to textbook exercises in Chapter 8 of Class 10 Mathematics to help them comprehend the problems presented in the chapter. In these NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4, students can find all the formulas they need to thoroughly understand the subject. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 can also help them prepare for other competitive exams and examinations. These solutions also aid the students to understand question patterns, mark distributions, and other topics.

3. How do NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 differ from other solutions?

Most of the NCERT solutions are curated by proficient mentors who have extensive knowledge of the concepts. To help students understand how to solve complex problems, each step is described in simple, easy-to-understand language. The NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 cover all the important topics, according to the most recent CBSE guidelines. The scheme of marks distribution is carefully considered while preparing NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. Students are encouraged to prepare for the board exams by using the NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4. For solutions, students can refer to NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.4 to prepare effectively for the examination.