# NCERT solutions for Class 12 Maths chapter 2 - Inverse Trigonometric Functions [Latest edition]

## Solutions for Chapter 2: Inverse Trigonometric Functions

Below listed, you can find solutions for Chapter 2 of CBSE, Karnataka Board PUC NCERT for Class 12 Maths.

Exercise 2.1Exercise 2.2Exercise 2.3
Exercise 2.1 [Pages 41 - 42]

### NCERT solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Exercise 2.1 [Pages 41 - 42]

Exercise 2.1 | Q 1 | Page 41

Find the principal values of sin^(-1) (-1/2)

Exercise 2.1 | Q 2 | Page 41

Find the principal value of  cos^(-1) (sqrt3/2)

Exercise 2.1 | Q 3 | Page 41

Find the principal value of cosec−1 (2)

Exercise 2.1 | Q 4 | Page 41

Find the principal value of tan^(-1) (-sqrt3)

Exercise 2.1 | Q 5 | Page 41

Find the principal value of  cos^(-1) (-1/2)

Exercise 2.1 | Q 6 | Page 41

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

Exercise 2.1 | Q 7 | Page 42

Find the principal value of  sec^(-1) (2/sqrt(3))

Exercise 2.1 | Q 8 | Page 42

Find the principal value of cot^(-1) (sqrt3)

Exercise 2.1 | Q 9 | Page 42

Find the principal value of  cos^(-1) (-1/sqrt2)

Exercise 2.1 | Q 10 | Page 42

Find the principal value of cosec^(-1)(-sqrt2)

Exercise 2.1 | Q 10 | Page 42

Find the value of  tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)

Exercise 2.1 | Q 12 | Page 42

Find the value of cos^(-1) (1/2) + 2 sin^(-1)(1/2)

Exercise 2.1 | Q 13 | Page 42

Find the value of if sin−1 y, then

A) 0 <= y < pi

B) -pi/2 <= y <= pi/2

c) 0 < y < pi

d) -pi/2 < y < pi/2

Exercise 2.1 | Q 14 | Page 42

Find the value of tan^(-1) sqrt3 - sec^(-1)(-2) is equal to

(A) π

(B) -pi/3

(C) pi/3

(D) (2pi)/3

Exercise 2.2 [Pages 47 - 48]

### NCERT solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Exercise 2.2 [Pages 47 - 48]

Exercise 2.2 | Q 1 | Page 47

Prove 3sin^(-1) x = sin^(-1)(3x - 4x^3), x in [-1/2, 1/2]

Exercise 2.2 | Q 2 | Page 47

Prove  3cos^(-1) x = cos^(-1)(4x^3 - 3x), x in [1/2, 1]

Exercise 2.2 | Q 3 | Page 47

Prove tan^(-1)  2/11 + tan^(-1)  7/24 = tan^(-1)  1/2

Exercise 2.2 | Q 4 | Page 47

Prove 2 tan^(-1)  1/2 + tan^(-1)  1/7 = tan^(-1)  31/17

Exercise 2.2 | Q 5 | Page 47

Write the function in the simplest form: tan^(-1)  (sqrt(1+x^2) -1)/x, x != 0

Exercise 2.2 | Q 6 | Page 47

Write the function in the simplest form: tan^(-1)  1/(sqrt(x^2 - 1)), |x| > 1

Exercise 2.2 | Q 7 | Page 47

Write the function in the simplest form: tan^(-1) (sqrt((1-cos x)/(1 + cos x))), x < pi

Exercise 2.2 | Q 8 | Page 47

Write the function in the simplest form:  tan^(-1)  ((cos x - sin x)/(cos x + sin x)) , 0 < x < pi

Exercise 2.2 | Q 9 | Page 48

Write the function in the simplest form: tan^(-1)  x/(sqrt(a^2 - x^2)), |x| < a

Exercise 2.2 | Q 10 | Page 48

Write the function in the simplest form: tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 <= x a/sqrt3

Exercise 2.2 | Q 11 | Page 48

Find the value of  tan^(-1) [2cos(2sin^(-1) 1/2)]

Exercise 2.2 | Q 12 | Page 48

Find the value of cot(tan^(-1) a + cot^(-1) a)

Exercise 2.2 | Q 13 | Page 48

Find the value of tan  1/2 [sin^(-1)  (2x)/(1+ x^2) + cos^(-1)  (1-y^2)/(1+y^2)], |x| < 1, y> 0  and xy < 1

Exercise 2.2 | Q 14 | Page 48

if sin(sin^(-1)  1/5 + cos^(-1) x)  = 1 then find the value of x

Exercise 2.2 | Q 15 | Page 48

if tan^(-1)  (x-1)/(x - 2) + tan^(-1)  (x + 1)/(x + 2) = pi/4 then find the value of x.

Exercise 2.2 | Q 16 | Page 48

Find the values of sin^(-1) (sin  (2pi)/3)

Exercise 2.2 | Q 17 | Page 48

Find the values of  tan^(-1) (tan  (3pi)/4)

Exercise 2.2 | Q 18 | Page 48

Find the values of  tan(sin^(-1)  3/5 + cot^(-1)  3/2)

Exercise 2.2 | Q 19 | Page 48

Find the values of  cos^(-1) (cos  (7pi)/6) is equal to

(A)  (7pi)/6

(B) (5pi)/6

(C) pi/3

(D) pi/6

Exercise 2.2 | Q 21 | Page 48

Find the values of sin(pi/3 - sin^(-1) (-1/2)) is equal to

(A) 1/2

(B) 1/3

(C) 1/4

(D) 1

Exercise 2.3 [Pages 51 - 52]

### NCERT solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Exercise 2.3 [Pages 51 - 52]

Exercise 2.3 | Q 1 | Page 51

Find the value of cos^(-1) (cos  (13pi)/6)

Exercise 2.3 | Q 2 | Page 51

Find the value of  tan^(-1) (tan  (7x)/6)

Exercise 2.3 | Q 3 | Page 51

Prove 2 sin^(-1)  3/5 = tan^(-1)  24/7

Exercise 2.3 | Q 4 | Page 51

Prove sin^(-1)  8/17 + sin^(-1)  3/5 = tan^(-1)  77/36

Exercise 2.3 | Q 5 | Page 51

Prove cos^(-1)  4/5 + cos^(-1)  12/13 = cos^(-1)  33/65

Exercise 2.3 | Q 6 | Page 51

Prove cos^(-1)  12/13 + sin^(-1)  3/5 = sin^(-1)  56/65

Exercise 2.3 | Q 7 | Page 51

Prove tan^(-1)  63/16 = sin^(-1)  5/13 + cos^(-1)  3/5

Exercise 2.3 | Q 8 | Page 51

Prove tan^(-1)   1/5 + tan^(-1)  (1/7) + tan^(-1)  1/3 + tan^(-1)  1/8 = pi/4

Exercise 2.3 | Q 9 | Page 52

Prove tan^(-1) sqrtx = 1/2 cos^(-1) ((1-x)/(1+x)) , x in [0, 1]

Exercise 2.3 | Q 10 | Page 52

Prove cot^(-1)  ((sqrt(1+sin x) + sqrt(1-sinx))/(sqrt(1+sin x) - sqrt(1- sinx))) = x/2, x in (0, pi/4)

Exercise 2.3 | Q 11 | Page 52

Prove tan^(-1)  ((sqrt(1+x) - sqrt(1-x))/(sqrt(1+x) + sqrt(1-x))) = pi/4 - 1/2 cos^(-1) x. - 1/sqrt(2) <= x <= 1 [Hint: put x =  cos 2 theta]

Exercise 2.3 | Q 12 | Page 52

Prove (9pi)/8 - 9/4  sin^(-1)  1/3 = 9/4 sin^(-1)  (2sqrt2)/3

Exercise 2.3 | Q 13 | Page 52

Solve 2 tan^(-1) (cos x) =  tan^(-1) (2 cosec x)

Exercise 2.3 | Q 14 | Page 52

Solve the following equation for x:

tan−1((1-x)/(1+x))-1/2 tan−1x = 0, where x > 0

Exercise 2.3 | Q 15 | Page 52

Solve sin (tan–1 x), | x| < 1 is equal to

(A) x/(sqrt(1-x^2))

(B) 1/sqrt(1-x^2)

(C) 1/sqrt(1+x^2)

(D) x/(sqrt(1+ x^2))

Exercise 2.3 | Q 16 | Page 52

Solve sin–1 (1 – x) – 2 sin–1 x = pi/2 then x is equal to

(A) 0, 1/2

(B) 1, 1/2

(C) 0

(D) 1/2

Exercise 2.3 | Q 17 | Page 52

Solve  tan^(-1) -  tan^(-1)  (x - y)/(x+y) is equal to

(A) pi/2

(B). pi/3

(C) pi/4

(D) (-3pi)/4

## Solutions for Chapter 2: Inverse Trigonometric Functions

Exercise 2.1Exercise 2.2Exercise 2.3

## NCERT solutions for Class 12 Maths chapter 2 - Inverse Trigonometric Functions

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Concepts covered in Class 12 Maths chapter 2 Inverse Trigonometric Functions are Inverse Trigonometric Functions (Simplification and Examples), Properties of Inverse Trigonometric Functions, Graphs of Inverse Trigonometric Functions, Inverse Trigonometric Functions - Principal Value Branch, Basic Concepts of Inverse Trigonometric Functions.

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