CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter 2 – Inverse Trigonometric Functions

In this article, we are providing you NCERT Exemplar Solutions for all the questions of Class 12 Mathematics Chapter 2 – Inverse Trigonometric Functions.

About NCERT Exemplar Solutions Class 12 Maths:

After the detailed analysis of some previous years’ question papers of board and engineering entrance exams, we have noticed that questions are frequently asked from NCERT Exemplar.

The experienced Subject Experts of Mathematics have explained all the questions of the chapter Inverse Trigonometric Functions in a very detailed manner to helps students to score good marks in board exams as well as competitive exams.

Questions from NCERT Exemplar Class 12 Mathematics are likely to be asked again in upcoming exams.

CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter- Application of Integrals

Types and number of questions in this chapter:

Few problems along with their solutions from this chapter are given follows:

Question:

The domain of the function cos ^-1(2x - 1) is

(a) [0, 1]                           

(b) [- 1, 1]                        

(c) (-1, 1)                         

(d) [0, π]

Solution: (a)

We have, cos^-1 (2x - 1)

Now, we know that the domain of cos ^-1(x) is - 1 ≤ x ≤1

⇒ - 1 ≤ 2x - ≤ 1  

Adding 1 to all terms, we get

⇒ 0 ≤ 2x ≤ 2

Dividing all terms by 2, we get

⇒ 0 ≤ x ≤ 1

⇒ x ∈ [0, 1]

Question:

The value of cot^-1 (- x) for all x ∈ R terms of cot^-1 x is ............  .

Solution:

We know that, cot^-1 (- x) = p - cot^-1 x, x ∈ R

Question:

All trigonometric functions have inverse over their respective domains.

Solution: False

Yes, all trigonometric functions have inverse over their respective domains.

Question:

The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.

Solution: True

Yes, the domain of trigonometric functions can be restricted in their domain to obtain their inverse functions.

Question:

The least numerical value, either positive or negative of angle q is called principal value of the inverse trigonometric function.

Solution: True

We know that, the principal value of an inverse trigonometric function which lies in its principal value branch. For the examples the principle value branch of inverse sin function is given by [−π/2, π/2].

Therefore, the smallest numerical value, either positive or negative of angle q is called the principal value of the function.

Question:

The graph of inverse trigonometric function can be obtained from the graph of their corresponding function by interchanging X and Y - axes.

Solution: True

If we interchange the coordinates of all the points in the graph of any trigonometric function, then we will get the graph of an inverse function of the respective function.

In other words, the graph of inverse trigonometric function is a mirror image (i.e., reflection) along the line y = x of the corresponding trigonometric function

Link to Download NCERT Exemplar Solutions for Class 12 Mathematics: Chapter 2 – Inverse Trigonometric Functions

About NCERT Exemplar Book Class 12 Maths:

NCERT Exemplar Class 12 Maths book is published by NCERT. Students must practice the questions given in these books as the level of these questions matches the difficulty level of the questions generally asked in engineering entrance exams. It will surely help students to score good marks in board exams as well as competitive exams. Each chapter of NCERT Exemplar Class 12 Maths book starts with a brief overview of the chapter followed by solved examples and unsolved exercises.

Students can download the complete NCERT Exemplar book from the link given below:

NCERT Exemplar Book Class 12 Maths: Inverse Trigonometric Functions

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