Answer each of the following questions in one word or one sentence or as per exact requirement of the question: Write the difference between maximum and minimum values of sin –1 x for x ∈ [–1, 1].

RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12^th

Q. No. 2 of Very short answer

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2

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the difference between maximum and minimum values of sin^–1x for x ∈ [–1, 1].

Let f (x) = sin^-1 x

For x to be defined, -1 ≤ x ≤ 1

For -1 ≤ x ≤ 1, sin^-1 (-1) ≤ sin^-1 x ≤ sin^-1 (1)

⇒ -π/2 ≤ sin^-1 x ≤ π/2

⇒ -π/2 ≤ f (x) ≤ π/2

Maximum value = π/2 and minimum value = -π/2

∴ The difference between maximum and minimum values of sin^-1 x = π/2 – (-π/2) = 2π/2

= π

Chapter Exercises

Exercise 4.1

Exercise 4.2

Exercise 4.3

Exercise 4.4

Exercise 4.5

Exercise 4.6

Exercise 4.7

Exercise 4.8

Exercise 4.9

Exercise 4.10

Exercise 4.11

Exercise 4.12

Exercise 4.13

Exercise 4.14

Very short answer

MCQ

1

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

2

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the difference between maximum and minimum values of sin^–1x for x ∈ [–1, 1].

3

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If , then write the value f x + y + z.

4

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If x > 1, then write the value of in terms of tan^–1 x.

5

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If x < 0, then write the value of in terms of tan^–1 x.

6

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Writ the value of for x > 0.

7

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of for x < 0.

8

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
What is the value of ?

9

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If –1 < x < 0, then write the value of .

10

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Writ the value of sin (cot^–1 x).

11

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

12

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the range of tan^–1x.

13

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of cos^–1(cos 1540°).

14

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of sin^–1 (sin(–600°)).

15

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

16

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of sin^–1(1550°).

17

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Evaluate: .

18

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Evaluate: .

19

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

20

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

21

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of cos^–1(cos 350°) – sin^–1(sin 350°).

22

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

23

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If , then write the value of x + y + xy.

24

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of cos^–1 (cos 6).

25

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

26

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

27

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

28

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

29

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

30

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

31

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Show that .

32

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Evaluate: .

33

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If , find x.

34

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If , then find x.

35

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

36

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If 4sin^–1 x + cos^–1 x = π, then what is the value of x?

37

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If x < 0, y < 0 such that xy = 1, then write the value of tan^–1 x + tan^–1 y.

38

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
What is the principal value of ?

39

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the principal value of .

40

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the principal value of .

41

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

42

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the principal value of .

43

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

44

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the principal value of .

45

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the principal value of cos^–1(cos 680°).

46

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

47

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

48

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of .

49

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of

50

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of the expression , when .

51

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the principal value of .

52

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
The set of values of .

53

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of for x < 0 in terms of cot^–1(x).

54

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of cot^–1(–x) for all x ∈ R in terms of cot^–1x.

55

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the value of , when .

56

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If , find the value of x.

57

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Find the value of .

58

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
If , find the value of x.

59

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Find the value of .

60

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Find the value of .

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