NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 Inverse Trigonometric Functions in Hindi and English Medium updated and modified for academic session 2024-25. The questions of 12th Maths ex. 2.2 are rearranged as per new NCERT textbook published for 2024-25 board exams.

## Class 12 Maths Exercise 2.2 Solutions in Hindi and English Medium

### NCERT Solutions for Class 12 Maths Exercise 2.2

Class: 12 | Mathematics |

Chapter 2: | Exercise 2.2 |

Chapter Name: | Inverse Trigonometric Functions |

Content: | NCERT Exercise Solution |

Content Mode: | Images, Online Videos and Text Format |

Medium: | English and Hindi Medium |

#### 12th Maths Exercise 2.2 Solutions

NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 Inverse Trigonometric Functions in English Medium Online as well as Offline free to use.

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##### More about 12 Maths Exercise 2.2

Exercise 2.2 contains the questions based on sin 2x, sin 3x, cos 3x, etc. used in class 11 trigonometry. It also includes the questions based on simplification of inverse trigonometric functions with square roots on the basis of the formula 1 – cos x = 2 sin² x/2 and 1 + cos x = 2 cos² x/2.

Question number 14 and 15 are the solutions of trigonometric functions. After solving the function, we should test the result whether it is satisfying the equation or not, then we have to finalize the answer.

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### Which examples and questions are the most important in exercise 2.2 of class 12th Maths for the board first term exams?

Exercise 2.2 of class 12th Maths has 6 examples (Examples 3, 4, 5, 6, 7, 8) and 21 questions. All the examples and questions of this exercise are essential to do. But examples 3, 5, 6 and questions 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 18, 19, 20, 21 of exercise 2.2 of class 12th Maths are the most important examples and questions for the board exams because these examples and questions have already been asked in the exams several times.

### How many days are needed to complete exercise 2.2 of grade 12th Maths?

If students can give 2 hours per day to exercise 2.2 of class 12th Maths, they need 3-4 days to complete exercise 2.2 of class 12th Maths. This time is an approximate time. This time can vary because no students can have the same working speed, efficiency, capability, etc.

### Is exercise 2.2 of class 12th Maths complex for first term exam?

Exercise 2.2 of class 12th Maths is not easy and not complex. It lies in the mid of easy and tough because some examples and questions of this exercise are easy, and some are complicated. However, the difficulty level of any topic/question varies from child to child. So, exercise 2.2 of class 12th Maths is easy, or tough depends on children also. Some children find it difficult, some find it easy, and some find it in the middle of easy and difficult.

### What are the main topics to focus in exercise 2.2 of class 12th Maths?

In exercise 2.2 of class 12th Maths, students will learn properties of inverse trigonometric functions and solve questions with the help of these properties.

Properties of inverse trigonometric functions are:

- 1. (i) sin⁻¹(1/x) = cosec⁻¹x, x ≥ 1 or x ≤ – 1

(ii) cos⁻¹(1/x) = sec⁻¹x, x ≥ 1 or x ≤ – 1

(iii) tan⁻¹(1/x) = cot⁻¹x, x > 0 - 2. (i) sin⁻¹(–x) = – sin⁻¹x, x ∈ [– 1, 1]

(ii) tan⁻¹(–x) = – tan⁻¹x, x ∈ R

(iii) cosec⁻¹(–x) = – cosec⁻¹x, | x | ≥ 1 - 3. (i) cos⁻¹(–x) = π – cos⁻¹x , x ∈ [– 1, 1]

(ii) sec⁻¹(–x) = π – sec⁻¹x, | x | ≥ 1

(iii) cot⁻¹(–x) = π – cot⁻¹x, x ∈ R - 4. (i) sin⁻¹x+ cos⁻¹x = π/2 , x ∈ [– 1, 1]

(ii) tan⁻¹x+ cot⁻¹x = π/2, x ∈ R

(iii) cosec⁻¹x+ sec⁻¹x = π/2, | x | ≥ 1 - 5. (i) tan⁻¹x + tan⁻¹y = tan⁻¹(x + y/1 – xy) , xy < 1 (ii) tan⁻¹x – tan⁻¹y = tan⁻¹(x – y/1 + xy) , xy > – 1

(iii) tan⁻¹x+ tan⁻¹y = π + tan⁻¹(x + y/1 – xy), xy > 1; x, y > 0 - 6. (i) 2 tan⁻¹x = sin⁻¹(2x/1+ x²) , | x | ≤ 1

(ii) 2 tan⁻¹x = cos⁻¹(1- x²/1+ x²), x ≥ 0

(iii) 2 tan⁻¹x = tan⁻¹(2x/1-x²), – 1 < x < 1