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

## Chapter 2 - Inverse Trigonometric Functions

#### Pages 41 - 42

Q 1 | Page 41

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

Q 2 | Page 41

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

Q 3 | Page 41

Find the principal value of cosec−1 (2)

Q 4 | Page 41

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

Q 5 | Page 41

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

Q 6 | Page 41

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

Q 7 | Page 42

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

Q 8 | Page 42

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

Q 9 | Page 42

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

Q 10 | Page 42

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

Q 10 | Page 42

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

Q 12 | Page 42

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

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

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

#### Pages 47 - 48

Q 1 | Page 47

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

Q 2 | Page 47

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

Q 3 | Page 47

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

Q 4 | Page 47

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

Q 5 | Page 47

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

Q 6 | Page 47

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

Q 7 | Page 47

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

Q 8 | Page 47

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

Q 9 | Page 48

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

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

Q 11 | Page 48

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

Q 12 | Page 48

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

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

Q 14 | Page 48

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

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.

Q 16 | Page 48

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

Q 17 | Page 48

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

Q 18 | Page 48

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

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

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

#### Pages 51 - 52

Q 1 | Page 51

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

Q 2 | Page 51

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

Q 3 | Page 51

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

Q 4 | Page 51

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

Q 5 | Page 51

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

Q 6 | Page 51

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

Q 7 | Page 51

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

Q 8 | Page 51

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

Q 9 | Page 52

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

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)

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]

Q 12 | Page 52

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

Q 13 | Page 52

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

Q 14 | Page 52

Solve tan^(1)  (1-x)/(1 + x) = 1/2 tan^(-1) x , (x > 0)

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))

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

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

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

NCERT solutions for Class 12 Mathematics chapter 2 (Inverse Trigonometric Functions) include all questions with solution and detail explanation from Mathematics Textbook for Class 12 Part 1. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has created the CBSE Mathematics Textbook for Class 12 Part 1 solutions in a manner that help students grasp basic concepts better and faster.

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

Using NCERT solutions for Class 12 Mathematics by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 12 prefer NCERT Textbook Solutions to score more in exam.

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