# Xam Idea Class 12 Maths Chapter 2 Solutions: Inverse Trigonometric Functions

Xam Idea Class 12 Maths Solutions for Chapter 2 ‘Inverse Trigonometric Functions’ is the best practice guide for you to prepare for CBSE Class 12 board exams. This guide carries the solutions of all the questions of ‘Inverse Trigonometric Functions’ of Xam Idea textbook. These solutions are prepared by our subject experts and will help you get knowledge on the restrictions of domain and ranges of trigonometric functions. You will see the behaviour of these restrictions through graphical representations. You will also get to learn about some elementary properties along with examples. Just follow our solutions for your board exam preparation, you will be given different methods through which questions could be solved.

Xam Idea Class 12 Maths Solutions for Inverse Trigonometric Functions give you 75 problems with solutions for practice. These questions are of three types – very short questions, short answer type questions, and long answer type questions. The questions cover the major topics that are explained in this chapter. You will be asked to find the principal value of Inverse trigonometric functions, some proving based questions and also questions where you need to compare trigonometric values. In order to solve these questions at once, you must be aware of the inverse trigonometric Identities. Keep practising more and more with these solutions and you will be able to solve any questions related to inverse trigonometry in CBSE Board exams.

Instasolv’s solutions can act as perfect assistance for you whenever you stumble in some questions Inverse Trigonometric Functions. We have given accurate solutions for all Xam Idea questions in a stepwise manner. Our Mathematics subject experts also provide you with the study notes for Xam Idea Class 12 Inverse Trigonometric Functions in plain language that will aid you to understand all the concepts associated with the chapter. We have framed the solutions in accordance with the latest CBSE syllabus for Class 12 Maths. Try our solutions for once and see how they change your way of learning.

## Important Topics of Xam Idea Class 12 Maths Solutions Chapter 2: Inverse Trigonometric Functions

**What are Inverse Trigonometric Functions?**

If you are aware of trigonometric functions, then it will be easy for you to understand the Inverse trigonometric functions. Simply, you can say them the inverse of trigonometric functions, and in other words, they are considered as **Arcus** Functions. Arcus functions are symbolized by writing an arc before functions like arcsine, arccosine, arctangent, respectively. Let’s see its graphical representation-

**Graph of arcsine**

See here the graph of sin^{-1} x

**Graph of arccosine**

We have a graph of inverse cosine function as given below-

**Graph of arctangent**

**Graph of arcCotangent**

We have a graph of the inverse of the cotangent function. See, the representation below-

**Graph of arcSecant**

The inverse graph of trigonometric function secant is given below-

**Graph of arcCosecant**

See here the graphical representation of the inverse function of cosecant

**Domain and Ranges of Inverse Trigonometric functions-**

Function | Domain | Range of an Inverse Function |

sin -1 x (arcsin x) | -1≤ x ≤1 | -π /2 ≤ y ≤ π /2 |

cos -1 x (arcosinex) | -1≤ x ≤1 | 0 ≤ y ≤ π |

tan -1 x (arctangent x) | – ∞ < x < ∞ | -π /2 < y < π /2 |

cot -1 x (arcotangente) | – ∞ < x < ∞ | 0 < y < π |

sec -1 x (arcsecant) | – ∞ ≤ x ≤ -1 or 1≤ x ≤ ∞ | 0 ≤ y ≤ π, y ≠ π /2 |

cosec -1 x (arccosecant) | – ∞ ≤ x ≤ -1 or 1≤ x ≤ ∞ | -π /2 ≤ y ≤ π /2, y ≠ 0 |

Considering the domain and ranges we will see some formulas associated with the inverse trigonometric functions.

- Sin
^{-1}x = x , Sin^{-1 }y = y - Cos
^{-1}x = x , Cos^{-1 }y = y - Tan
^{-1}x = x , Tan^{-1}y= y - Cot
^{-1}x = x , Cot^{-1}y = y - Sec
^{-1}x = x , Sec^{-1}y = y - Cosec
^{-1}x = x , Cosec^{-1}y = y

**Derivatives of Inverse Trigonometric Functions-**

You will learn some derivatives of Inverse Trigonometric functions in this chapter. It will help you in solving questions of this chapter.

Apart from this, you will come across some identities in this chapter-

- Sin-1x + Cos-1x = π/2
- Tan-1x + Cot-1x = π/2
- Cosec-1x + Sec-1x = π/2

### Exercise Discussion of Xam Idea Class 12 Maths Solutions Chapter 2: Inverse Trigonometric Functions

Inverse Trigonometric Functions of Xam Idea Solutions Class 12 Maths book has a total of 75 questions, categorized into three sections.

**Very Short Questions**

- There are 21 total very short questions, that are further grouped into two parts. Part 1 has 16 questions previous year questions whereas the other part has 5 very short answer questions.
- Usually, you will have questions, at which you need to find the principal values of inverse trigonometric functions.
- There are some questions at which an inverse trigonometric equation has been given and you have to determine the value of x.
- Also, a question in which you have to show the range of one branch of Sin-1x other than the principal branch.

**Short Questions**

- You will have 11 questions in this section.
- In the first 7 questions, you will have inverse trigonometric equations, and you need to write them in simplest form. Also, questions on simplification of inverse trigonometric functions, and proving based as well.
- In the last 4 questions, you will be able to solve value-based questions in which you have to find the value of x.

**Long Answer Type Questions**

- In this section, you will have 44 questions carved up into 33 are PYQs (Previous Year Questions.
- You will have 16 questions on proving based, you need to go through the important identities and derivatives formulas to counter them.
- Also, you will have 1 question at which, you need to identify the greater among tan(1) and tan-1(1).

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