Contents

These Solutions are part of NCERT Solutions for Class 12 Maths . Here we have given NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 12 |

Subject |
Maths |

Chapter |
Chapter 2 |

Chapter Name |
Inverse Trigonometric Functions |

Exercise |
Ex 2.1, Ex 2.2 |

Number of Questions Solved |
35 |

Category |
NCERT Solutions |

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

### Chapter 2 Inverse Trigonometric Functions Exercise 2.1

**Question 1-10.**

**Find the principal values of the following:**

**(1) **

**(2) **

**(3) **

**(4) **

**(5) **

**(6) **

**(7) **

**(8)**

**(9) **

**(10) **

**Solution:**

(1) Let = y

∴

the range of principal value of sin^{-1} is

**Question 11-12.**

**Find the principal values of the following:**

**(11) **

**(12) **

**Solution:**

(11)

Now tan^{-1} (1) =

∴the range of principal value branch of

**Question 13.**

**If sin ^{-1} x = y, then**

**(a) 0 ≤ y ≤ π**

**(b)**

**(c) 0 < y < π**

**(d)**

**Solution:**

The range of principal value of sin is

∴ if sin

^{-1}x = y then

Option (b) is correct

**Question 14.**

** is equal to**

**(a) π**

**(b) **

**(c) **

**(d) **

**Solution:**

∴ Principal values of sec^{-1} is [0,π] –

Option (b) is correct

### Chapter 2 Inverse Trigonometric Functions Exercise 2.2

**Question 1.**

**Solution:**

Let sin^{-1} x = θ

sin θ = x sin 3θ = 3 sin θ – 4 sin³ θ

sin 3θ = 3x – 4x³

3θ = sin^{-1 }(3x – 4x³)

or

**Question 2.**

**Solution:**

Let cos^{-1} x = θ

x = cos θ

R.H.S= cos^{-1} (4x³ – 3cosx)

= cos^{-1} (4 cos³θ – 3 cosθ)

= cos^{-1} (cos 3θ) [∴ cos 3θ = 4 cos³ θ – 3 cos θ]

= 3θ

= 3 cos^{-1} x

= L.H.S.

**Question 3.**

**Solution:**

L.H.S =

=

=

= R.H.S

**Question 4.**

**Solution:**

L.H.S =

**Question 5.**

**Write the function in the simplest form**

**Solution:**

Putting x = θ

∴ θ = tan^{-1} x

**Question 6.**

**Solution:**

Given expression

Let x = secθ

**Question 7.**

**Solution:**

=

**Question 8.**

**Solution:**

Dividing numerator and denominator by cos x

**Question 9.**

**Solution:**

Let x = a sinθ

=> = sinθ

**Question 10.**

**Solution:**

Put x = a tanθ,

we get

**Question 11.**

**Find the value of the following**

**Solution:**

=

**Question 12.**

**cot[tan ^{-1} a + cot^{-1} a]**

**Solution:**

Given

cot[tan

^{-1}a + cot

^{-1}a]

=

**Question 13.**

**Solution:**

Putting x = tanθ

=> tan^{-1} x = θ

**Question 14.**

**If then find the value of x**

**Solution:**

**Question 15.**

**If then find the value of x**

**Solution:**

L.H.S

**Question 16.**

**Solution:**

=

=

**Question 17.**

**Solution:**

=

=

**Question 18.**

**Solution:**

Let

sinθ =

**Question 19.**

** is equal to**

**(a) **

**(b) **

**(c) **

**(d) **

**Solution:**

=

**Question 20.**

** is equal to**

**(a) **

**(b) **

**(c) **

**(d) 1**

**Solution:**

**Question 21.**

** is equal to**

**(a) π**

**(b) **

**(c) 0**

**(d) 2√3**

**Solution:**

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