Solution of Chapter 2. Inverse Trigonometric Functions (Mathematics - Exemplar Book)

Exercise

1

Find the value of.
2

Evaluate .
3

Prove that cot ( pi /4 - 2cot^-13 ) = 7
4

Find the value of .
5

Find the value of .
6

Show that .
7

Find the real solution of the equation:
8

Find the value of .
9

If , then show that , where n is any integer.
10

Show that .
11

Solve the following equation .
12

Prove that

13

Find the simplified form of

cos^-1 ( 3/5 cosx + 4/5 sinx ), where xin[ - 3 pi /4 , pi /4 ].
14

Prove that .
15

Show that

16

Prove that .
17

Find the value of .
18

Show that and, justify why the other value is ignored.
19

If is an arithmetic progression with common difference d, then evaluate the following expression.
20

Which of the following in the principal value branch of.
21

Which of the following in the principal value branch of.
22

If , then x equals to
23

The value of is
24

The domain of the function is
25

The domain of the function defined by is
26

If cos then x is equal to
27

The value of sin (2tan–1 (.75)) is equal to
28

The value of cos–1 is equal to
29

The value of the expression 2 sec–1 2 + sin–1 is
30

If tan–1 x + tan–1 y = 4π/5, then cot–1x + cot–1 y equals
31

If where a, x ϵ] 0, 1, then the value of x is
32

The value of cot cos^-1 7/25 is
33

The value of the expression tan is
34

If |x| ≤ 1, then 2 tan–1 x + sin–1 is equal to
35

If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β (γ + α) + γ (α + β) equals
36

The number of real solutions of the equatio is
37

If cos–1x > sin–1 x, then
38

Fill in the blanks

The principal value of is ________.
39

Fill in the blanks

The value of is __________.
40

Fill in the blanks

If cos (tan–1x + cot–1 √3) = 0, then value of x is _________.
41

Fill in the blanks

The set of values of is _________.
42

Fill in the blanks

The principal value of tan–1 √3 is _________.
43

Fill in the blanks

The value of is ________.
44

Fill in the blanks

The value of cos (sin–1 x + cos–1 x), |x| ≤ 1 is ________.
45

Fill in the blanks

The value of expression when is_______.
46

Fill in the blanks

If y = 2 tan–1 x + sin–1 for all x, then ____ < y < ____.
47

Fill in the blanks

The result tan–1 x – tan–1( x-y/1+xy ) is true when value of xy is _________.
48

Fill in the blanks

The value of cot–1(–x) for all x ϵ R in terms of cot–1 x is _______.
49

State True or False for the statement

All trigonometric functions have inverse over their respective domains.
50

State True or False for the statement

The value of the expression (cos–1x)2 is equal to sec2 x.
51

State True or False for the statement

The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
52

State True or False for the statement

The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
53

State True or False for the statement

The graph of inverse trigonometric function can be obtained from the graph of their corresponding trigonometric function by interchanging x and y axes.
54

State True or False for the statement

The minimum value of n for which tan^-1 n/pi > pi /4 , n inn is valid is 5.
55

State True or False for the statement

The principal value of is