#### Online Mock Tests

#### Chapters

Chapter 2: Complex Numbers

Chapter 3: Theory of Equations

Chapter 4: Inverse Trigonometric Functions

Chapter 5: Two Dimensional Analytical Geometry-II

Chapter 6: Applications of Vector Algebra

Chapter 7: Applications of Differential Calculus

Chapter 8: Differentials and Partial Derivatives

Chapter 9: Applications of Integration

Chapter 10: Ordinary Differential Equations

Chapter 11: Probability Distributions

Chapter 12: Discrete Mathematics

## Chapter 4: Inverse Trigonometric Functions

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 4 Inverse Trigonometric Functions Exercise 4.1 [Page 137]

Find all the values of x such that – 10π ≤ x ≤ 10π and sin x = 0

Find all the values of x such that Find all the values of x such that −3π ≤ x ≤ 3π and sin x = −1

Find the period and amplitude of y = sin 7x

Find the period and amplitude of y = `- sin(1/3 x)`

Find the period and amplitude of y = 4 sin(– 2x)

Sketch the graph of y = `sin(1/3 x)` for 0 ≤ x ≤ 6π

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

Find the value of `sin^-1 (sin((5pi)/4))`

For what value of x does sin x = sin^{–1}x?

Find the domain of the following

`f(x) = sin^-1 ((x^2 + 1)/(2x))`

Find the domain of the following

`g(x) = 2sin^-1(2x - 1) - pi/4`

Find the value of `sin^-1(sin (5pi)/9 cos pi/9 + cos (5pi)/9 sin pi/9)`

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 4 Inverse Trigonometric Functions Exercise 4.2 [Pages 142 - 143]

Find all values of x such that – 6π ≤ x ≤ 6π and cos x = 0

Find all values of x such that – 5π ≤ x ≤ 5π and cos x = 1

State the reason for `cos^-1 [cos(- pi/6)] ≠ - pi/6`

Is cos^{–1}(– x) = π – cos^{–1} true? justify your answer

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

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

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

Find the value of `cos-1 [cos pi/7 cos pi/17 - sin pi/7 sin pi/17]`

Find the domain of `f(x) = sin^-1 ((|x| - 2)/3) + cos^-1 ((1 - |x|)/4)`

Find the domain of `g(x) = sin^-1x + cos^-1x`

For what value of x, the inequality `pi/2 < cos^-1 (3x - 1) < pi` holds?

Find the value of `cos[cos^-1 (4/5) + sin^-1(4/5)]`

Find the value of `cos^-1(cos((4pi)/3)) + cos^-1 (cos((5pi)/4))`

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 4 Inverse Trigonometric Functions Exercise 4.3 [Pages 147 - 148]

Find the domain of the following functions:

`tan^-1 (sqrt(9 - x^2))`

Find the domain of the following functions:

`1/2 tan^-1 (1 - x^2) - pi/4`

Find the value of `tan^-1(tan (5pi)/4)`

Find the value of `tan^-1 (tan(- pi/6))`

Find the value of `tan(tan^-1((7pi)/4))`

Find the value of `tan(tan^-1(1947))`

Find the value of `tan(tan^-1(- 0.2021))`

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

Find the value of `sin(tan^-1 (1/2) - cos^-1 (4/5))`

Find the value of `cos(sin^-1 (4/5) - tan^-1 (3/4))`

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 4 Inverse Trigonometric Functions Exercise 4.4 [Pages 154 - 155]

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

Find the principal value of `cot^-1 (sqrt(3))`

Find the principal value of `"cosec"^-1 (- sqrt(2))`

Find the value of `tan^-1 (sqrt(3)) - sec^-1 (- 2)`

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

Find the value of `cot^-1(1) + sin^-1 (- sqrt(3)/2) - sec^-1 (- sqrt(2))`

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 4 Inverse Trigonometric Functions Exercise 4.5 [Page 166]

Find the value, if it exists. If not, give the reason for non-existence

`sin^-1 (cos pi)`

Find the value, if it exists. If not, give the reason for non-existence

`tan^-1(sin(- (5pi)/2))`

Find the value, if it exists. If not, give the reason for non-existence

`sin^-1 [sin 5]`

Find the value of the expression in terms of x, with the help of a reference triangle

sin (cos^{–1}(1 – x))

Find the value of the expression in terms of x, with the help of a reference triangle

cos (tan^{–1} (3x – 1))

Find the value of the expression in terms of x, with the help of a reference triangle

`tan(sin^-1(x + 1/2))`

Find the value of `sin^-1[cos(sin^-1 (sqrt(3)/2))]`

Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`

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

Prove that `tan^-1 2/11 + tan^-1 7/24 = tan^-1 1/2`

Prove that `sin^-1 3/5 - cos^-1 12/13 = sin^-1 16/65`

Prove that `tan^-1x + tan^-1y + tan^-1z = tan^-1[(x + y + z - xyz)/(1 - xy - yz - zx)]`

If tan^{–1}x + tan^{–}^{1}y + tan^{–}^{1}z = π, show that x + y + z = xyz

Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`

Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`

Solve: `sin^-1 5/x + sin^-1 12/x = pi/2`

Solve: `tan^-1x = cos^-1 (1 - "a"^2)/(1 + "a"^2) - cos^-1 (1 - "b"^2)/(1 + "b"^2), "a" > 0, "b" > 0`

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

Solve: `cot^-1 x - cot^-1 (x + 2) = pi/12, x > 0`

Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`

### Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide Chapter 4 Inverse Trigonometric Functions Exercise 4.6 [Pages 166 - 168]

#### MCQ

Choose the correct alternative:

The value of sin^{–1}(cos x), 0 ≤ x ≤ π is

`pi - x`

`x - pi/2`

`pi/2 - x`

`x - pi`

Choose the correct alternative:

If `sin^-1x + sin^-1y = (2pi)/3` ; then `cos^-1x + cos^-1y` is equal to

`(2pi)/3`

`pi/3`

`pi/6`

`pi`

Choose the correct alternative:

`sin^-1 3/5 - cos^-1 13/13 + sec^-1 5/3 - "cosec"^-1 13/12` is equal to

`2pi`

`pi`

0

`tan^-1 12/65`

Choose the correct alternative:

If sin^{–1}x = 2sin^{–}^{1} α has a solution, then

`|alpha| ≤ 1/sqrt(2)`

`|alpha| ≥ 1/sqrt(2)`

`|alpha| < 1/sqrt(2)`

`|alpha| > 1/sqrt(2)`

Choose the correct alternative:

`sin^-1(cos x) = pi/2 - x` is valid for

`pi ≤ x ≤ 0`

0 ≤ x ≤ π

`- pi/2 ≤ x ≤ pi/2`

`- pi/4 ≤ x ≤ (3pi)/4`

Choose the correct alternative:

If sin^{-1} x + sin^{-1} y + sin^{-1} z = `(3pi)/2`, the value of show that `x^2017 + y^2018 + z^2019 - 9/(x^101 + y^101 + z^101)` is

0

1

2

3

Choose the correct alternative:

If `cot^-1x = (2pi)/5` for some x ∈ R, the value of tan^{-1} x is

`- pi/10`

`pi/5`

`pi/10`

`- pi/5`

Choose the correct alternative:

The domain of the function defined by f(x) = `sin^-1 sqrt(x - 1)` is

[1, 2]

[– 1, 1]

[0, 1]

[– 1, 0]

Choose the correct alternative:

If x = `1/5`, the value of `cos(cos^-1x + 2sin^-1x)` is

`- sqrt(24/25)`

`sqrt(24/25)`

`1/5`

`- 1/5`

Choose the correct alternative:

`tan^-1 (1/4) + tan^-1 (2/9)` is equal to

`1/2 cos^-1 (3/5)`

`1/2 sin^-1 (3/5)`

`1/2 tan^-1 (3/5)`

`tan^-1 (1/2)`

Choose the correct alternative:

If the function `f(x) = sin^-1 (x^2 - 3)`, then x belongs to

[– 1, 1]

`[sqrt(2), 2]`

`[-2, sqrt(2)] ∪ [sqrt(2), 2]`

`[- 2 -sqrt(2)]`

Choose the correct alternative:

If cot^{–1}2 and cot^{–}^{1}3 are two angles of a triangle, then the third angle is

`pi/4`

`(3pi)/4`

`pi/6`

`pi/3`

Choose the correct alternative:

`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation

x

^{2}– x – 6 = 0x

^{2}– x – 12 = 0x

^{2}+ x – 12 = 0x

^{2}+ x – 6 = 0

Choose the correct alternative:

sin^{–1}(2 cos^{2}x – 1) + cos^{–}^{1}(1 – 2 sin^{2}x) =

`pi/2`

`pi/3`

`pi/4`

`pi/6`

Choose the correct alternative:

If `cot^-1(sqrt(sin alpha)) + tan^-1(sqrt(sin alpha))` = u, then cos 2u is equal to

tan

^{2}α0

– 1

tan 2α

Choose the correct alternative:

If |x| ≤ 1, then `2tan^-1x - sin^-1 (2x)/(1 + x^2)` is equal to

tan

^{–1}xsin

^{–}^{1}x0

π

Choose the correct alternative:

The equation tan^{–1}x – cot^{–}^{1}x = `tan^-1 (1/sqrt(3))` has

no solution

unique solution

two solutions

infinite number of solutions

Choose the correct alternative:

If `sin^-1x + cot^-1 (1/2) = pi/2`, then x is equal to

`1/2`

`1/sqrt(5)`

`2/sqrt(5)`

`sqrt(3)/5`

Choose the correct alternative:

If `sin^-1x + "cosec"^-1 5/4 = pi/2`, then the value of x is

4

5

2

3

Choose the correct alternative:

sin(tan^{–1}x), |x| < 1 is equal to

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

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

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

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

## Chapter 4: Inverse Trigonometric Functions

## Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide chapter 4 - Inverse Trigonometric Functions

Tamil Nadu Board Samacheer Kalvi solutions for Class 12th Mathematics Volume 1 and 2 Answers Guide chapter 4 (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 Tamil Nadu Board of Secondary Education Class 12th Mathematics Volume 1 and 2 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 12th Mathematics Volume 1 and 2 Answers Guide chapter 4 Inverse Trigonometric Functions are Some Fundamental Concepts, Sine Function and Inverse Sine Function, The Cosine Function and Inverse Cosine Function, The Tangent Function and the Inverse Tangent Function, The Cosecant Function and the Inverse Cosecant Function, The Secant Function and Inverse Secant Function, The Cotangent Function and the Inverse Cotangent Function, Principal Value of Inverse Trigonometric Functions, Properties of Inverse Trigonometric Functions, Inverse Trigonometric Functions.

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