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

Mathematics Textbook for Class 12

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Chapters

NCERT Mathematics Class 12

Mathematics Textbook for Class 12

Chapter 2: Inverse Trigonometric Functions

Chapter 2: Inverse Trigonometric Functions solutions [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`

Chapter 2: Inverse Trigonometric Functions solutions [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

Chapter 2: Inverse Trigonometric Functions solutions [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`

Chapter 2: Inverse Trigonometric Functions

NCERT Mathematics Class 12

Mathematics Textbook for Class 12

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

NCERT solutions for Class 12 Maths chapter 2 (Inverse Trigonometric Functions) include all questions with solution and detail explanation. 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 the CBSE Mathematics Textbook for Class 12 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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 Class 12 solutions Inverse Trigonometric Functions exercise 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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