NCERT Solutions for Class 9 Political Science Chapter 2

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**NCERT Solutions for Class 12 Maths Chapter 2**: The NCERT Solutions for Class 12 Chapter 2 deals with Inverse Trigonometric Functions. Students might already have some basic idea about Trigonometric from their previous classes. In Class 12, students will be learning more advanced concepts of Inverse Trigonometric Functions. Practicing NCERT Solutions can be a great way to prepare for competitive exams. Students should go through all exercises to score higher marks.

Students can refer to the Class 12 Maths Maths Chapter 2 NCERT Solutions to better understand the subject. Designed by professional academics at Embibe, the NCERT Solutions can be one of the best ways to prepare for the exam. It will play an important role in helping the students prepare for the exams. Students can refer to the article to download Chapter 2 NCERT Maths Class 12 Solutions. Read further to find the download link.

The NCERT Class 12 Maths textbook and solutions contain important details about Chapter 2. The solutions have detailed step-by-step solved solutions that the students can refer to. Designed by the top academic experts at Embibe, the Class 12 Maths Chapter 2 NCERT Solutions can help students prepare for the exams.

When the students are stuck while solving any problem related to the chapter, they can refer to NCERT Solutions. Professionals design these NCERT Solutions following the latest CBSE and NCERT guidelines. Students can refer to the section below to download the NCERT Class 12 Maths Inverse Trigonometric Functions Solutions.

**Q.1. Find the principal value of sin-1-12**

**Solution:** Let y=sin-1-12

=sin-1-sinπ6 ∵sinπ6=12

=-sin-1sinπ6 ∵sin-1(-x)=-sin-1(x) ∀x∈-1,1 =-π6 ∵sin-1(siny)=y, if -π/2≤y≤π/2 We know that the range of sin-1x is -π2,π2,

and -π6∈-π2,π2 Hence, the principal value of sin-1-12 is -π6.

**Q.2. Find the principal value of cosec-1-2.**

**Solution: **Let cosec-1-2=y, then

cosec y=-2=-cosecπ4=cosec-π4

We know that the range of the principal value of cosec-1x is -π2,π2-0 and cosec-π4=-2

Hence, the principal value of cosec-1-2 is -π4.

**Q.3. Find the value of tan-11+cos-1-12+sin-1-12.**

**Solution:** Let tan-11=x, then tanx=1=tanπ4

We know that the range of the principal value of tan-1x is -π2,π2

Therefore, tan-11=π4

Let cos-1-12=y, then

cosy=-12=-cosπ3=cosπ-π3=cos2π3

We know that the range of the principal value of cos-1x is 0,π

Therefore, cos-1-12=2π3

Let sin-1-12=z, then

sinz=-12=-sinπ6=sin-π6

We know that the range of the principal value of sin-1x is -π2,π2

Therefore, sin-1-12=-π6

Now,

tan-11+cos-1-12+sin-1-12

=π4+2π3-π6=3π+8π-2π12=9π12=3π4

Students have already had a basic idea about the type of questions that will come in the exam. They can refer to the link given below to download the Class 12 Maths Chapter 2 NCERT Solutions. Click on the link to download the solutions and start practicing for the exams.

Inverse Trigonometric Functions come under the unit, Relations and Functions, which carry a weightage of 10 marks. The chapter deals with the graph and formulas of the trigonometric functions such as sine, cosine, tangent, cotangent, secant and cosecant.

Students will have to focus on the different operations to be done on these trigonometric functions. These topics are helpful for the students to understand the concepts related to Physics, Geometry, Engineering and Navigation.

Some of the important questions from class 12 Maths chapter 2 – Inverse Trigonometric Functions are as under:

Important Previous Year Important Questions For Inverse Trigonometric Functions 1. Determine the principal value of cos ^{-1}( -1/2) 2. Find the value of cot (tan ^{-1} α + cot^{-1} α) 3. Find the value of tan ^{-1} √3 – sec^{-1}(–2) is equal to(A) π (B) – π/3 (C) π/3 (D) 2π/3 4. Prove that sin ^{-1} (3/5) – sin^{-1} (8/17) = cos^{-1} (84/85) 5. Find the value of cos ^{-1} (1/2) + 2 sin^{-1} (1/2) 6. Find the principal value of tan ^{-1} (1)7. If tan ^{-1} (x − 1)/(x − 2) + tan^{-1} (x + 1)/(x + 2) = ?/4 , then find the value of x.8. Solve tan ^{-1} 2x + tan^{-1} 3x = π/4 |

Some other important questions from “Inverse trigonometric functions” chapter are given below:

The concepts included in the Inverse Trigonometric Functions chapter are tabulated below:

Ex 2.1 | Introduction |

Ex 2.2 | Basic Concepts |

Ex 2.3 | Properties of Inverse Trigonometric Functions |

In Chapter 1, you have studied that the inverse of a function f, denoted by f^{–1}, exists if f is one-one and onto. Many functions are not one-one, onto or both; hence, we can not talk of their inverses. In Class XI, you have learned that trigonometric functions are not one-one and onto over their natural domains and ranges, and hence, their inverses do not exist.

In this chapter, you will study the restrictions on domains and ranges of trigonometric functions that ensure the existence of their inverses and observe their behaviour through graphical representations. Besides, some elementary properties will also be discussed. The inverse trigonometric functions play an important role in Calculus, for they serve to define many integrals. Also, the concepts of inverse trigonometric functions are used in science and engineering.

**Q.1: Where can I find NCERT Solutions for Class 12 Maths Chapter 2 online? ****Ans.** You can find Class 12 Maths Chapter 2 Solutions PDF for free on Embibe.

**Q.2: What are the topics covered in NCERT Solutions For Class 12 Maths Chapter 2 PDF?****Ans:** The main topics of NCERT Class 12 Chapter 2 is:

(i) NCERT Solutions For Class 12 Maths Chapter 2 Exercise 2.1: Introduction

(ii) NCERT Solutions For Class 12 Maths Chapter 2 Exercise 2.2: Basic Concepts

(iii) NCERT Solutions For Class 12 Maths Chapter 2 Exercise 2.3: Properties of Inverse Trigonometric Functions

**Q.3: Are the NCERT 12th Maths Ch 2 solutions provided by Embibe free?Ans.** Yes, all NCERT solutions provided by Embibe are free to download. You do not even have to register or signup.

**Q.4: Can the NCERT Class 12 Maths be helpful for exam preparation?Ans:** Yes. The NCERT Class 12 Maths can play an important role in helping students prepare for the exam. The students must thoroughly refer to the NCERT solutions to score higher marks in the exam.

**Q.5: Where can I get NCERT Class 12 Maths Solutions?****Ans**: Students can get all NCERT Solutions for Class 12 Maths from Embibe for free.