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NCERT Solutions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 2-Inverse Trigonometric Functions provided by us are in an easy and simple language for you to understand the concept quickly.  This chapter consists of various topics on inverse trigonometric functions such as introduction to the inverse trigonometric function, domain and range of inverse trigonometric functions, the graph of inverse trigonometric functions and properties of inverse trigonometric functions. Apart from these, this chapter also includes the trigonometric equation and solution or roots of a trigonometric equation.

Our NCERT Solutions cover all the topics and sub-topics of CBSE Class 12 Maths Syllabus chapter 2 in a step by step manner. Each concept of this chapter is interlinked with each other, so you have to focus on all the parts of the chapter. Our NCERT Solutions help you do just that. Our NCERT Solutions are structured well to help you grasp even the most difficult concepts quickly.  

This chapter consists of 2 exercises and one miscellaneous exercise. On the whole, there are around 35 questions at the end of the chapter. Inverse Trigonometric Functions answer all questions. They help you enhance your conceptual foundation and help you excel in various competitive exams.

CBSE NCERT Class 12 Maths Chapter 2

Our NCERT Solutions for Class 12 Maths Chapter 2-Inverse Trigonometric Functions discuss the inverse of a function f which is denoted by f–1.  Some of the important points and formulas covered in this chapter have been given below.

  • Inverse Circular Function

This part of Inverse Trigonometric Function discusses the inverse circular function explained below.

Consider two functions, y = f(x) and x = g(y) 

Then, f (g(y)) = y and g (f(y)) = x, here f and y are said to be inverse of each other

i.e., g = f-1 

IF y = f(x), then x = f-1 (y)

  • Inverse Trigonometric Function

This section of NCERT Class 12 Maths Chapter 2 explains to you about the similarities of other trigonometric functions. 

Example: 

If y = sin X-1 , then x = sin-1 y, similarly for other trigonometric functions. This is called the inverse trigonometric function.

  • Domain and range of inverse trigonometric functions Graph of inverse trigonometric functions

In this section of NCERT CBSE Class 12 Maths Chapter 2 help, you will learn about the graphical representation of trigonometry. The same has been represented below.

The below-given table explains the functions, abbreviation and the relationship to sides of a right triangle. This also explains the six important trigonometric functions. 

Functions

Abbreviation Relationship to sides of a right triangle

Sine Function

sin

Opposite side/ Hypotenuse

Tangent Function

tan

Opposite side / Adjacent side

Cosine Function

cos

Adjacent side / Hypotenuse

Cosecant Function

cosec

Hypotenuse / Opposite side

Secant Function

sec

Hypotenuse / Adjacent side

Cotangent Function cot

Adjacent side / Opposite side

 

  • Properties of Inverse Triangle

This section of CBSE NCERT Class 12 Maths Book, explains various properties that are followed in the Inverse Triangle.

  • Trigonometry Angles

This part of the chapter explains the angles which are represented as 0°, 30°, 45°, 60° and 90°

For Example: In a right-angled triangle,

Sin θ = Perpendicular/Hypotenuse

or θ = sin-1 (P/H)

Therefore,

θ = cos-1 (Base/Hypotenuse)

θ = tan-1 (Perpendicular/Base)

  • Trigonometry Table

The table below explains the common angles which will be used in trigonometric problems which are related to ratios.

Angles

30° 45° 60° 90°

Sin θ

0 ½ 1/√2 √3/2

1

Cos θ 1 √3/2 1/√2 ½

0

Tan θ

0 1/√3 1 √3

Cosec θ

2 √2 2/√3

1

Sec θ

1 2/√3 √2 2

Cot θ

√3

1

1/√3

0

 

  • Trigonometry Formulas

In NCRT CBSE Class 12 Maths Chapter 2, you will learn about the Trigonometric formulas that are derived in the case of Right-Angled Triangles. Some of the important trigonometric identities are as mentioned below.

  1. Pythagorean Identities
    sin² θ + cos ² θ = 1
    tan 2 θ + 1 = sec2 θ
    cot2θ + 1 = cosec 2θ
    sin 2θ = 2 sin θ cos θ
    cos 2θ = cos² θ – sin² θ
    tan 2θ = 2 tan θ / (1 – tan² θ)
    cot 2θ = (cot² θ – 1) / 2 cot θ
  2. Sum and Difference identities-
    For angles u and v, we have the following relationships:
    sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
    cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
    tan(u+v) = tan(u) + tan(v)/ 1tan(u) tan(v)
    sin(u – v) = sin(u)cos(v) – cos(u)sin(v)
    cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
    tan(u-v) =  tan(u) tan(v)/ 1+tan(u) tan(v)
     
  3. If A, B and C are angles and a, b and c are the sides of a triangle, then,

Sine Laws 

  1. a/sinA = b/sinB = c/sinC

Cosine Laws

  1. c2 = a2 + b2 – 2ab cos C
  2. a2 = b2 + c2 – 2bc cos A
  3. b2 = a2 + c2 – 2ac cos B

The later part of Class 12 Maths Inverse Trigonometric Functions explains about the unit circle, which is also a part of the trigonometry table.

Class 12 Maths Inverse Trigonometric Functions Exercise Questions

There are a total of 2 exercises at the end of the chapter, which consists of 31 questions in total. There is also a miscellaneous exercise at the end of the chapter. Our NCERT Solutions for Class 12 Maths Chapter 2- Inverse Trigonometric Functions answer all questions of all exercises in details. Below is a brief overview:

Exercise 2.1: 

  • All the questions in this exercise are similar, where you will have to find the principal values of the given functions. To solve these questions, you will have to be thorough with the trigonometry formulas.

Exercise 2.2:

  • Questions 1 to 15 is similar types of questions, in which you have to find the smallest value of the given function and find the value of x. Here, the major focus is on trigonometric angles. 
  • Questions 16 to 18 are similar questions where you have to find the values of the given expression. 

Miscellaneous Exercise

There is one miscellaneous exercise which is given at the end of the chapter, which consists of 17 questions. The questions cover all the concepts of the chapter. These questions ask you to prove the given functions. They are mostly application-based questions.

Benefits of NCERT CBSE Class 12 Maths Chapter 2

Our NCERT Solutions for Class 12 Maths Chapter 2- Inverse Trigonometric Functions come with a number of learning advantages that you can leverage from. Some of them have been listed below.

  • Our eminent Maths experts have answered all the questions of all exercises with a hundred per cent accuracy, and they are easy to understand. 
  • All the concepts are covered as per the updates given by NCERT and CBSE. 
  • Our NCERT Solutions are well-structured, systematic and follow a logical flow to facilitate easy, quick and effective learning.
  • They have been specially devised to help you become easily and promptly become thorough with the chapter and score high marks in your board exams.
  • They give you ample practice and help you gain the confidence to answer any question type from the chapter in your board exams. 
  • Our Maths shortcuts and innovative study techniques will ensure you remember more and score more in your exams.
  • They keep your concepts clear and assist you in building a strong knowledge base.