Samacheer Kalvi solutions for Mathematics - Volume 1 and 2 [English] Class 12 TN Board chapter 4 - Inverse Trigonometric Functions [Latest edition]

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^–1x?

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)`

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))`. 

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))`

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))`

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^–1x + tan^–1y + tan^–1z = 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)`

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

If cot^–12 and cot^–13 are two angles of a triangle, then the third angle is

Choose the correct alternative:

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

Choose the correct alternative:

sin^–1(2 cos²x – 1) + cos^–1(1 – 2 sin²x) =

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

sin(tan^–1x), |x| < 1 is equal to