# NCERT Solutions for Class 12 Maths Chapter 2

NCERT Solutions for class 12 Maths Chapter 2 Inverse Trigonometric Functions in Hindi & English Medium PDF form to free download along with NCERT Solutions Apps. The Previous Years Papers are to know the type and pattern of the questions asked which are designed as per latest CBSE Syllabus for the current academic session.

 Class: 12 Subject: Maths – गणित Chapter 2: Inverse Trigonometric Functions

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## NCERT Solutions for class 12 Maths Chapter 2

Download the solutions of class xii maths chapter 2 Hindi as well as English Medium free to use online or in PDF form including miscellaneous exercise and practice books with solutions and answers.

### Solutions of NCERT Hindi & English Medium

• 12 Maths Chapter 2 Exercise 2.1 Solutions
• 12 Maths Chapter 2 Exercise 2.2 Solutions
• 12 Maths Chapter 2 Miscellaneous Exercise 2 Solutions

### Assignments for practice

#### Mixed Chapter Tests

Chapter 1, 2, 3 & 4

##### Level 3 Test 1 Test 2

Inverse Trigonometric Functions
We know that a function has inverse if and only if it is one – one and onto. There are many functions like trigonometric functions are not one – one or onto because these functions periodic so these are many one. In order to get inverse of these functions, we must restrict their domain and co-domain in such a way that they become one – one and onto and these restricted values are known as principle values.

There are some important theorems/ properties of inverse trigonometric functions. It is important to know that how to convert one function into the terms of others.

Complement functions are useful during the conversion of one functions into it complimentary functions.

During the application of addition formula of tan, we should know that whether the product of x and y is greater than 1 or not. If it is more than 1, use the above formula and then apply the following formula.

Historical Facts!
The study of trigonometric functions started in 2nd millennium BC but in India it flourished in the Gupta Period due to Aryabhata. During the middle age, the study of trigonometry continued in Islamic Maths. The modern form of trigonometry functions were being used since 17th century by famous mathematician Isaac Newton, James Stirling etc.

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#### Find the principal value of 〖sin〗^(-1) (-1/2)

Let 〖sin〗^(-1) (-1/2)=y,
then sin y =-1/2=-sin(π/6)=sin(-π/6)
We know that the range of the principal value branch of sin−1 is [-π/2,π/2] and sin(-π/6)=-1/2
Therefore, the principal value of sin^(-1) (-1/2) is -π/6.

#### निम्नलिखित को सिद्ध कीजिए: 3〖sin〗^(-1) x=〖sin〗^(-1) (3x-4x^3 ), x∈[-1/2,1/2].

माना, 〖sin〗^(-1) x = θ, तब x = sin θ.,
RHS = 〖sin〗^(-1) (3x-4x^3 )
=〖sin〗^(-1) (3 sin⁡θ-4〖sin〗^3 θ)
=〖sin〗^(-1) (sin⁡3θ )
= 3θ
= 3〖sin〗^(-1) x
= LHS

#### Find the principal value of tan−1 (−1).

Let tan−1 (−1) = y. Then, tan⁡〖y=-1=-tan(π/4)=tan(-π/4)〗
We know that the range of the principal value branch of tan−1 is (-π/2,π/2) and tan(-π/4)=-1
Therefore, the principal value of tan−1 (−1) is -π/4.

#### Solve for x: 2〖tan〗^(-1) (cos⁡x )=〖tan〗^(-1) (2cosec⁡x )

Given that 2〖tan〗^(-1) (cos⁡x )=〖tan〗^(-1) (2cosec⁡x )
⇒〖tan〗^(-1) (2cos⁡x/(1-〖cos〗^2 x))=〖tan〗^(-1) (2cosec⁡x )
[as 2〖tan〗^(-1) x
=〖tan〗^(-1) 2x/(1-x^2 )] ⇒ 2cos⁡x/(1-〖cos〗^2 x)=2cosec⁡x
⇒ 2cos⁡x/(〖sin〗^2 x)=2/sin⁡x
⇒2 sin⁡〖x.cos⁡〖x=2〖sin〗^2 x〗 〗
⇒ 2 sin⁡〖x.cos⁡〖x-2〖sin〗^2 x=0〗 〗
⇒2 sin⁡〖x(cos⁡〖x-sin⁡x 〗 )=0〗
⇒ 2 sin⁡〖x=0 or cos⁡〖x-sin⁡x 〗=0〗
But sin⁡x≠0 as it does not satisfy the equation
〖∴cos〗⁡〖x-sin⁡x 〗=0
⇒cos⁡〖x=sin⁡x
⇒tan⁡〖x=1〗 〗
∴x= π/4

#### यदि sin(〖sin〗^(-1) 1/5+〖cos〗^(-1) x)=1, तो x का मान ज्ञात कीजिए।

दिया है: sin(〖sin〗^(-1) 1/5+〖cos〗^(-1) x)=1
⇒(〖sin〗^(-1) 1/5+〖cos〗^(-1) x)=〖sin〗^(-1) 1
⇒(〖sin〗^(-1) 1/5+〖cos〗^(-1) x)=π/2
⇒〖sin〗^(-1) 1/5 =〖sin〗^(-1) x
[∵ 〖sin〗^(-1) x+〖cos〗^(-1) x=π/2] ⇒x=1/5

## 1 thought on “NCERT Solutions for Class 12 Maths Chapter 2”

1. Santosh Ahirwal says:

Nice