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NCERT solutions Mathematics Class 12 Part 1 chapter 2 Inverse Trigonometric Functions

Chapters

NCERT Mathematics Class 12 Part 1

Mathematics Textbook for Class 12 Part 1

Chapter 2 - Inverse Trigonometric Functions

Pages 41 - 42

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

Q 1 | Page 41

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

Q 2 | Page 41

Find the principal value of cosec−1 (2)

Q 3 | Page 41

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

Q 4 | Page 41

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

Q 5 | Page 41

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

Q 6 | Page 41

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

Q 7 | Page 42

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

Q 8 | Page 42

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

Q 9 | Page 42

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

Q 12 | 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 13 | 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`

Q 14 | Page 42

Pages 47 - 48

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

Q 1 | Page 47

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

Q 2 | Page 47

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

Q 3 | Page 47

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

Q 4 | Page 47

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

Q 5 | Page 47

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

Q 6 | Page 47

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

Q 7 | Page 47

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

Q 8 | Page 47

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

Q 9 | 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 10 | Page 48

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

Q 11 | Page 48

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

Q 12 | 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 13 | Page 48

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

Q 14 | Page 48

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

Q 15 | Page 48

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

Q 16 | Page 48

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

Q 17 | Page 48

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

Q 18 | 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 19 | 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

Q 21 | Page 48

Pages 51 - 52

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

Q 1 | Page 51

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

Q 2 | Page 51

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

Q 3 | Page 51

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

Q 4 | Page 51

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

Q 5 | Page 51

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

Q 6 | Page 51

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

Q 7 | Page 51

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

Q 8 | Page 51

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

Q 9 | 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 10 | 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 11 | Page 52

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

Q 12 | Page 52

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

Q 13 | Page 52

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

Q 14 | 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 15 | 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 16 | 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`

Q 17 | Page 52

NCERT Mathematics Class 12 Part 1

Mathematics Textbook for Class 12 Part 1
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