Home > NCERT Solutions > NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 (Ex 2.1)

NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 (Ex 2.1)

Mathematics in Class 11 and 12 can be tough, however, the benefits that it brings forth are noteworthy. Mathematics is an extremely significant subject. Therefore, it is a good idea to take up Mathematics. Mathematics opens a huge number of career opportunities for students. Even students from Humanities and Medical streams take up Mathematics to keep a secondary, safe career path. Going through the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 will help the students enhance their understanding.

CBSE Class 12 Syllabus for Mathematics is quite interesting and engaging. Students are recommended to go through the syllabus of Class 12 Mathematics before starting to learn the chapters in Class 12. Mathematics requires in-depth knowledge of each topic. It is important to solve exercises given in the textbook from time to time. There are many examples given in the NCERT textbook of Class 12 Mathematics related to each topic to help students easily understand the applications of formulae and enhance their understanding of topics. To solve the Ex 2.1 Class 12th, students are required to apply exact formulas learned in Class 12 Chapter 2. Students having problems in solving 12th Maths 2.1 questions can access NCERT Solutions For Class 12 Maths Chapter 2 Exercise 2.1 from Extramarks website and mobile application.

Students need to practice effectively for a subject like Mathematics. The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 can be downloaded for boosting the board exam preparation. The latest CBSE board syllabus for Mathematics comprises six units, which are as follows:-

Relations and Functions
Algebra
Calculus
Vectors and Three-Dimensional Geometry
Linear Programming
Probability

Unit 1 is about Relations and Functions has two subparts to it which are:-

Relations and Functions
Inverse Trigonometric Functions

In Chapter 2, the primary focus is on part b i.e. Inverse Trigonometric Functions. The Chapter in question here dwells upon the study of the uses and Scopes of Trigonometric Functions that result in their Inverses, and analyse their conduct through Graphical Representations. Certain fundamental aspects of Trigonometric functions are also explained in this chapter. Even in Calculus, these Trigonometric functions pose as crucial tools as they help in defining many Integrals. The Relations and Functions unit carries good weightage in the CBSE Board Mathematics Paper. The syllabus mentions that the topics to cover under Inverse Trigonometric Functions are:-

Definition
Range
Domain
Principal Value Branch

Graphs of Inverse Trigonometric Functions
Elementary Properties of Inverse Trigonometric Functions

The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 is based on the concept of the Inverse Trigonometric Function. The application of these methods aids students in attaining good marks in their examinations. The provided solutions match the guidelines of CBSE regarding NCERT. Students should read through the entire answer to properly understand each step and have conceptual clarity.

NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 (Ex 2.1)

The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 provided by Extramarks is curated by Extramarks experts in a tactical way so that the solutions are easy to understand and also to the point. The step-by-step explanation and the amount of explanatory time associated with each question are highly reasonable and time-efficient. Some students usually question the importance of solving the NCERT exercises and tend to overlook them. The exercise questions help solve questions in the Mathematics board exam. Students from the Central Board of Secondary Education (CBSE) can access the solutions for all classes from the Extramarks’ website and mobile application. Extramarks has solutions for the following classes-

NCERT Solutions Class 12

NCERT Solutions Class 11

NCERT Solutions Class 10

NCERT Solutions Class 9

NCERT Solutions Class 8

NCERT Solutions Class 7

NCERT Solutions Class 6

NCERT Solutions Class 5

NCERT Solutions Class 4

NCERT Solutions Class 3

NCERT Solutions Class 2

NCERT Solutions Class 1

Inverse Trigonometric Functions can be somewhat challenging to understand, therefore, it is likely that students look for answers to grasp the theories and tactics behind each answer. Students are advised to solve the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 for all clarifications.

The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 is helpful for students in all aspects of Ex 2.1 Class 12. Class 12 students’ initial learning along with detailed explanations lead to a renewed enthusiasm and understanding of the topic at hand. Going through the solutions is important for students to go one step further on the path to their goals. Practising the questions given in Exercise 2.1 helps build conceptual understanding effectively. There are fourteen questions in Exercise 2.1 and all of them are crucial from the board exam perspective.

Students can access the Class 12 Math Ex 2.1 Solution from Extramarks’ website and mobile application and continue their Mathematics board exam preparation. It is necessary to devise a unique study plan for studying Mathematics in Class 12. Students need to practice all the questions given in the textbook after learning a particular topic. Extramarks provides NCERT Solutions for all chapters of Class 12 Mathematics.

When preparing for the Class 12 Mathematics examination, it is important to solve sample question papers and past years’ papers of Mathematics. Past years’ papers help in understanding the marking scheme of Class 12 Mathematics. Apart from NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1, students can access past years’ papers in Mathematics from the Extramarks’ website and mobile application in PDF format. To prepare well for Mathematics chapters, students can attend live classes on Extramarks’ website and mobile application. Students can get answers to all of their doubts in the Class 12 Mathematics chapters. The Class 12 students of the CBSE Board can attend mock tests related to each chapter to prepare for board exams efficiently.

About Class 12 NCERT Chapter 2 Inverse Trigonometric Functions Exercise 2.1

Access NCERT Solutions for Class 12 Mathematics Chapter 2 – Inverse Trigonometric Functions

NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 can be accessed from the Extramarks’ website and mobile application in PDF format.

Benefits of NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1

Extramarks aims to help students who need assistance in any subject with the highest quality of uniform knowledge. The purpose of Extramarks is to help students achieve better results in exams by maximizing their learning potential. Extramarks ensures that no stone is left unturned to make all concepts crystal clear to students by bringing forth relevant and very accurate answers through the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1

The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 are solved such in a manner that students can easily find accurate answers to Exercise 2.1 questions and enhance their ongoing study. The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 are easily understandable. The solutions are properly presented just below each question so that students can easily access them. Students’ preparation time is saved, along with their brainpower. The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 guides students to secure better marks in examinations and tests of Mathematics.

The error-free solutions are the result of the hard work of team members comprising expert teachers and scholars. Therefore, NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 are reliable and error-free. All provided solutions are perfect and do not require cross-examination or double-check. Hence, students need not go anywhere else to understand a concept ever again. Students need to take a good look into the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 and start preparing.

Extramarks helps students in getting higher marks in their board exams. The entire curriculum of Class 12 is made by experts and professional teachers. Exact explanations about every topic, every chapter, and every theory are included in the study course for students. The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 are well explained for students. Class 12 CBSE Board students can access all the NCERT solutions that they require along with explanations and lectures. The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 are extremely easy to access. The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 are curated by Extramarks’ team of professional teachers. Not only NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1, but Extramarks also provides solutions for all NCERT exercises and numerous model papers. Solving exercise questions with the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 helps improve answer writing skills for Mathematics subjects.

Why choose Extramarks?

Countless websites have put forth NCERT solutions and model papers. However, Extramarks is extremely uncomplicated and concise, both in terms of solved papers, exercises and test series. Students need to gear up for board exams, as higher marks in Class 12 Board results will help them throughout their life. Board exam results help in getting admissions to many good colleges, and performing well in board examinations helps secure higher marks in the entrance exams of colleges. Studying carefully assists the students during entrance exam preparations. It is essential to go through the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 carefully. Students of Class 12 Central Board of Secondary Education (CBSE) can download all solutions and explanations of various chapters of Class 12 Mathematics. Practising with the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 helps understand the marking scheme of the Mathematics subject.

The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 are provided for students in the best possible way. Students need to study every part of the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 carefully so that students can also use all key points in their answers. The students are expected to learn each topic one by one and solve exercise questions related to each topic. The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 contains solutions to all the questions in the NCERT Class 12 Mathematics Chapter 2 Exercise 2.1.\

Access Other Exercises of Class 12 Maths Chapter 2

Chapter 2 Inverse Trigonometric Functions Exercises
Exercise 2.2	20 Questions & Solutions (4 Short Answers, 16 Long Answers)

Q.1 Find the principal values of the following

$\sin^{- 1} (- \frac{1}{2})$

Ans

$\begin{array}{l} Let \sin^{- 1} (- \frac{1}{2}) = x . Then, sinx = - \frac{1}{2} . \\ We know that the range of the principal value branch of \sin^{- 1} is \\ [- \frac{π}{2}, \frac{π}{2}] and \sin (\frac{π}{6}) = \frac{1}{2} . \\ Therefore, principal value of \sin^{- 1} (- \frac{1}{2}) = - \frac{π}{6} \end{array}$

Q.2 $\cos^{- 1} (\frac{\sqrt{3}}{2})$

Ans

$\begin{array}{l} Let \cos^{- 1} (\frac{\sqrt{3}}{2}) = x . Then, cosx = \frac{\sqrt{3}}{2} . \\ We know that the range of the principal value branch of \cos^{- 1} is \\ [0, π] and \cos (\frac{π}{6}) = \frac{\sqrt{3}}{2} . \end{array}$

Q.3 ${cosec}^{- 1} (2)$

Ans

$\begin{array}{l} Let {cosec}^{- 1} (2) = x . Then, cosecx = 2 . \\ We know that the range of the principal value branch of {cosec}^{- 1} is \\ [- \frac{π}{2}, \frac{π}{2}] - {0} and cosec (\frac{π}{6}) = 2 . \\ Therefore, principal value of {cosec}^{- 1} (2) = \frac{π}{6} \end{array}$

Q.4 ${tan}^{- 1} (- \sqrt{3})$

Ans

$\begin{array}{l} Let \tan^{- 1} (- \sqrt{3}) = x . Then, tanx = - \sqrt{3} . \\ We know that the range of the principal value branch of \tan^{- 1} is \\ (- \frac{π}{2}, \frac{π}{2}) and \tan (\frac{π}{3}) = \sqrt{3} . \\ Therefore, principal value of \tan^{- 1} (- \sqrt{3}) = - \frac{π}{3} . \end{array}$

Q.5 ${cos}^{- 1} (- \frac{1}{2})$

Ans

$\begin{array}{l} Let \cos^{- 1} (- \frac{1}{2}) = x . Then, cosx = - \frac{1}{2} . \\ We know that the range of the principal value branch of \cos^{- 1} is \\ [0, π] and \cos (\frac{π}{3}) = \frac{1}{2} . \\ cosx = - \frac{1}{2} \\ = - \cos (\frac{π}{3}) \\ = \cos (π - \frac{π}{3}) \\ = \cos (\frac{2 π}{3}) \\ \Rightarrow x = \frac{2 π}{3} \\ Therefore, principal value of \cos^{- 1} (- \frac{1}{2}) = \frac{2 π}{3} . \end{array}$

Q.6 ${tan}^{- 1} (- 1)$

Ans

$\begin{array}{l} Let \tan^{- 1} (- 1) = - 1 . \\ We know that the range of the principle value branch of \tan^{- 1} is \\ (- \frac{π}{2}, \frac{π}{2}) and \tan (\frac{π}{4}) = 1 . \\ Therefore, principle value of \tan^{- 1} (- 1) = - \frac{π}{4} \end{array}$

Q.7 ${sec}^{- 1} (\frac{2}{\sqrt{3}})$

Ans

$\begin{array}{l} Let \sec^{- 1} (\frac{2}{\sqrt{3}}) = x . Then, secx = \frac{2}{\sqrt{3}} . \\ We know that the range of the principal value branch of \cos^{- 1} is \\ [0, π] - \{\frac{π}{2}\} and \sec (\frac{π}{6}) = \frac{2}{\sqrt{3}} . \\ Therefore, principal value of \sec^{- 1} (\frac{2}{\sqrt{3}}) = \frac{π}{6} \end{array}$

Q.8 ${cot}^{- 1} (\sqrt{3})$

Ans

$\begin{array}{l} Let \cot^{- 1} (\sqrt{3}) = x . Then, cotx = \sqrt{3} . \\ We know that the range of the principal value branch of \cot^{- 1} is \\ (0, π) and \cot (\frac{π}{6}) = \sqrt{3} . \\ Therefore, principal value of \cot^{- 1} (\sqrt{3}) = \frac{π}{6} . \end{array}$

Q.9 ${cos}^{- 1} (- \frac{1}{\sqrt{2}})$

Ans

$\begin{array}{l} Let \cos^{- 1} (- \frac{1}{\sqrt{2}}) = x . Then, cosx = - \frac{1}{\sqrt{2}} . \\ We know that the range of the principal value branch of \cos^{- 1} is \\ [0, π] and \cos (\frac{π}{4}) = \frac{1}{\sqrt{2}} . \\ cosx = - \frac{1}{\sqrt{2}} \\ = - \cos (\frac{π}{4}) \\ = \cos (π - \frac{π}{4}) \\ = \cos (\frac{3 π}{4}) \\ \Rightarrow x = \frac{3 π}{4} \\ Therefore, principal value of \cos^{- 1} (- \frac{1}{2}) = \frac{3 π}{4} . \end{array}$

Q.10 $c o s e c^{- 1} (- \sqrt{2})$

Ans

$\begin{array}{l} Let {cosec}^{- 1} (- \sqrt{2}) = x . Then, cosecx = - \sqrt{2} . \\ We know that the range of the principal value branch of \\ {cosec}^{- 1} is [- \frac{π}{2}, \frac{π}{2}] - {0} and cosec (\frac{π}{4}) = \sqrt{2} . \\ Therefore, principal value of {cosec}^{- 1} (- \sqrt{2}) = - \frac{π}{4} \end{array}$

Q.11 Find the values of the following:

${tan}^{- 1} (1) + \cos^{- 1} - (\frac{1}{2}) + \sin^{- 1} (- \frac{1}{2})$

Ans

$\begin{array}{l} Given : \\ \tan^{- 1} (1) + \cos^{- 1} - (\frac{1}{2}) + \sin^{- 1} (- \frac{1}{2}) \\ We shall find the principal value of each term as given below : \\ Let \tan^{- 1} (1) = x . Then, tanx = 1 . \\ We know that the range of the principal value branch of \tan^{- 1} is \\ (- \frac{π}{2}, \frac{π}{2}) and t an (\frac{π}{4}) = 1 . \\ Therefore, principal value of \tan^{- 1} (1) = \frac{π}{4} . \\ second term : \\ Let \cos^{- 1} (- \frac{1}{2}) = x . Then, cosx = - \frac{1}{2} . \\ We know that the range of the principal value branch of \cos^{- 1} is \\ [0, π] and \cos (\frac{π}{3}) = \frac{1}{2} . \\ cosx = - \frac{1}{2} \\ = - \cos (\frac{π}{3}) \\ = \cos (π - \frac{π}{3}) \\ = \cos (\frac{2 π}{3}) \\ and third term : \\ Let \sin^{- 1} (- \frac{1}{2}) = x . Then, sinx = - \frac{1}{2} . \\ We know that the range of the principal value branch of \sin^{- 1} is \\ [- \frac{π}{2}, \frac{π}{2}] and \sin (\frac{π}{6}) = \frac{1}{2} . \\ Therefore, principal value of \sin^{- 1} (- \frac{1}{2}) = - \frac{π}{6} \\ Then, \\ \tan^{- 1} (1) + \cos^{- 1} (- \frac{1}{2}) + \sin^{- 1} (- \frac{1}{2}) = \frac{π}{4} + \frac{2 π}{3} - \frac{π}{6} \\ = \frac{3 π + 8 π - 2 π}{12} \\ = \frac{9 π}{12} \\ = \frac{3 π}{4} . \end{array}$

Q.12 ${cos}^{- 1} (\frac{1}{2}) + 2 \sin^{- 1} (\frac{1}{2})$

Ans

$\begin{array}{l} \cos^{- 1} (\frac{1}{2}) + 2 \sin^{- 1} (\frac{1}{2}) \\ First term : \cos^{- 1} (\frac{1}{2}) \\ Let \cos^{- 1} (\frac{1}{2}) = x . Then, cosx = \frac{1}{2} . \\ We know that the range of the principal value branch of \cos^{- 1} is \\ [0, π] and \cos (\frac{π}{3}) = \frac{1}{2} . \\ Therefore, principal value of \cos^{- 1} (\frac{1}{2}) = \frac{π}{3} \\ Second term : 2 \sin^{- 1} (\frac{1}{2}) \\ Let \sin^{- 1} (\frac{1}{2}) = x . Then, sinx = \frac{1}{2} . \\ We know that the range of the principal value branch of \sin^{- 1} is \\ [- \frac{π}{2}, \frac{π}{2}] and \sin (\frac{π}{6}) = \frac{1}{2} . \\ Therefore, \\ principal value of 2 \sin^{- 1} (\frac{1}{2}) = 2 \times \frac{π}{6} = \frac{π}{3} \\ ∴ \cos^{- 1} (\frac{1}{2}) + 2 \sin^{- 1} (\frac{1}{2}) = \frac{π}{3} + \frac{π}{3} \\ = \frac{2 π}{3} \end{array}$

Q.13

$\begin{array}{l} {Ifsin}^{- 1} x = y, then \\ A) 0 \leq y \leq π \\ B) - \frac{π}{2} \leq y \leq \frac{π}{2} \\ C) 0 < y < π \\ D) - \frac{π}{2} < y < \frac{π}{2} \end{array}$

Ans

$\begin{array}{l} Since, \sin^{- 1} : [- 1, 1] \to [- \frac{π}{2}, \frac{π}{2}] \\ So, option B is the correct answer . \end{array}$

Q.14

$\begin{array}{l} \tan^{- 1} \sqrt{3} - \sec^{- 1} (- 2) is equal to \\ (A) π \\ (B) - \frac{π}{3} \\ (C) \frac{π}{3} \\ (D) \frac{2 π}{3} \end{array}$

Ans

$\begin{array}{l} Given : \tan^{- 1} \sqrt{3} - \sec^{- 1} (- 2) \\ Since, \tan^{- 1} \sqrt{3} = \frac{π}{3}, and \\ let \sec^{- 1} (- 2) = x . Then, secx = - 2 . \\ We know that the range of the principal value branch of \sec^{- 1} is \\ [0, π] - \{\frac{π}{2}\} and \sec (\frac{π}{3}) = 2 . \\ ∴ secx = - 2 = - \sec (\frac{π}{3}) \\ = \sec (π - \frac{π}{3}) \\ = \sec (\frac{2 π}{3}) \\ Therefore, principal value of \sec^{- 1} (- 2) = \frac{2 π}{3} . \\ ∴ \tan^{- 1} \sqrt{3} - \sec^{- 1} (- 2) = \frac{π}{3} - (\frac{2 π}{3}) \\ = \frac{π - 2 π}{3} \\ = - \frac{π}{3} . \\ Option B is the correct answer . \end{array}$

Please register to view this section

FAQs (Frequently Asked Questions)

Authentic NCERT Solutions Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Exercise 2.1 are available on the Extramarks’ website and mobile application, they are accurate and precise. In NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1, the explanations are given in an easy-to-read format and all points and steps are explained and stated to students. The NCERT Solutions Class 12 Mathematics Chapter 2 Exercise 2.1 are created using the most recent CBSE standards and test specifications.

The NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 helps students in getting the most accurate solutions for each of the questions of Exercise 2.1. Getting NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1 is significant in making the initial concepts of Chapter 2 stronger in students’ minds.

NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 (Ex 2.1)

NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 (Ex 2.1)

About Class 12 NCERT Chapter 2 Inverse Trigonometric Functions Exercise 2.1

Access NCERT Solutions for Class 12 Mathematics Chapter 2 – Inverse Trigonometric Functions

Benefits of NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1

Why choose Extramarks?

Access Other Exercises of Class 12 Maths Chapter 2

Please register to view this section

FAQs (Frequently Asked Questions)

Company

Terms & Conditions

Resources

Teachers

NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 (Ex 2.1)

NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 (Ex 2.1)

About Class 12 NCERT Chapter 2 Inverse Trigonometric Functions Exercise 2.1

Access NCERT Solutions for Class 12 Mathematics Chapter 2 – Inverse Trigonometric Functions

Benefits of NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1

Why choose Extramarks?

Access Other Exercises of Class 12 Maths Chapter 2

Share

Please register to view this section

FAQs (Frequently Asked Questions)

1. Which online resource provides the NCERT Solutions Class 12 Maths Chapter 2 Exercise 2.1?

2. What are the most significant aspects of the NCERT Solutions Class 12 Mathematics Chapter 2 Exercise 2.1?

Share

Company

Terms & Conditions

Resources

Teachers