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).

RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12^th

Q. No. 24 of Very short answer

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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).

Given cos^-1 (cos 6)

We know that cos^-1 (cos θ) = 2π – θ, if θ ∈ [π, 2π]

= 2π – 6

∴ cos^-1 (cos 6) = 2π - 6

1

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

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Write the difference between maximum and minimum values of sin^–1x for x ∈ [–1, 1].

3

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If , then write the value f x + y + z.

4

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If x > 1, then write the value of in terms of tan^–1 x.

5

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If x < 0, then write the value of in terms of tan^–1 x.

6

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Writ the value of for x > 0.

7

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Write the value of for x < 0.

8

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What is the value of ?

9

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If –1 < x < 0, then write the value of .

10

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Writ the value of sin (cot^–1 x).

11

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Write the value of .

12

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Write the range of tan^–1x.

13

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Write the value of cos^–1(cos 1540°).

14

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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

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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

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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

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Write the value of .

21

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Write the value of cos^–1(cos 350°) – sin^–1(sin 350°).

22

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Write the value of .

23

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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

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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

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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

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Write the value of the expression , when .

51

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Write the principal value of .

52

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The set of values of .

53

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Write the value of for x < 0 in terms of cot^–1(x).

54

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Write the value of cot^–1(–x) for all x ∈ R in terms of cot^–1x.

55

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Write the value of , when .

56

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If , find the value of x.

57

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Find the value of .

58

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If , find the value of x.

59

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60

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