2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Students can Download 2nd PUC Maths Chapter 2 Inverse Trigonometric Functions Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

Karnataka 2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

2nd PUC Maths Inverse Trigonometric Functions One Mark Questions and Answers

Inverse Function Calculator: With the methods presented, the calculator will find the inverse of the provided function.

Question 1.
Find the principal value of the folowing:
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 1

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 2.
Write the domain of f(x) = sec-1x.
Answer:
R – (-1, 1).

Question 3.
Write the set of values of x for which 2 tan-1x = tan-1\(\frac{2 x}{1-x^{2}}\) holds.
Answer:
-1 < x < 1.

Question 4.
Write the range of the principal value branch of the function y = cosec-1 x.
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 2

Question 5.
Write the set of values of x for which 2 tan-1 x = Sin-1 \(\frac{2 x}{1+x^{2}}\) holds.
Answer:
|x| ≤ 1.

Question 6.
Write the set of values of x for which 2 tan-1 = cos-1\(\frac{1-x^{2}}{1+x^{2}}\) holds.
Answer:
x ≥ 0.

Question 7.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 3
Answer:
Let cos-1\(\frac { 1 }{ 2 }\) = θ ⇒ cos θ = \(\frac { 1 }{ 2 }\)
Considering principal branch θ ∈ [0, π ]
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 4

Question 8.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 5
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 6

Question 9.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 5
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 6

Question 10.
Find the domain of sin-1 (2x)
Answer:
Let sin-1 (2x) = 0 ⇒ 2x = sin 0
-1 ≤ sin θ ≤ 1 ⇒ -1 ≤ 2x ≤ 1
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 7

Question 11.
Write the range of the principal value branch of the function y = sin-1 x.
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 8

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

2nd PUC Maths Inverse Trigonometric Functions Two Marks Questions and Answers

Prove the following:

Question 1.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 9
Answer:
LHS = sin-1(\(\sqrt{1-x^{2}}\)) put x = sin θ ⇒ θ = sin-1 x
= sin-1 (2 sin θ \(\sqrt{1-\sin ^{2} \theta}\))
= sin-1 (2 sin θ cos θ)
= sin-1 (sin 2θ) = 2θ = 2 sin-1 x = RHS.

Question 2.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 10
Answer:
LHS = sin-1 (2x\(\sqrt{1-x^{2}}\)) putx = cos θ ⇒ θ = cos-1 x
= sin-1 (2 c0s θ \(\sqrt{1-\cos ^{2} \theta}\))
= sin-1 (2 sin θ cos θ)
= sin-1 (sin 2θ) = 2θ = 2 cos-1 x = RHS.

Question 3.
sin-1 (3x – 4x3) = 3 sin-1 x, x ∈ \(\left[-\frac{1}{2}, \frac{1}{2}\right]\)
Answer:
LHS = sin-1 (3x – 4x3)
put x = sin ⇒ θ = sin x
= sin-1 (3 sin θ – 4 sin3 θ)
= sin-1 (sin 3θ) = 3θ = 3 sin-1 x = RHS.

Question 4.
cos-1(4x2 – 3x) = 3 cos-1x, x ∈ \(\left[\frac{1}{2}, 1\right]\)
Answer:
LHS = cos-1(4x3 – 3x)
put x = cos θ ⇒ θ = cos-1 x
= cos-1 (4 cos3 θ – 3 cos θ)
= cos-1(cos 3θ) = 3θ = 3 cos-1x = RHS.

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 5.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 11
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 12

Question 6.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 13
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 14

Question 7.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 15
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 16

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 8.
tan-1\(\frac { 1 }{ 2 }\) + tan-1\(\frac { 2 }{ 11 }\) = tan-1\(\frac { 3 }{ 4 }\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 16

Question 9.
tan-1\(\frac { 2 }{ 11 }\) + tan-1\(\frac { 7 }{ 24 }\) = tan-1\(\frac { 1 }{ 2 }\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 18

Question 10.
tan-1\(\frac { 1 }{ 2 }\) + tan-1\(\frac { 1 }{ 3 }\) = \(\frac{\pi}{4}\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 19

Simplify the following

Question 1.
sin-1\(\left(\sin \frac{2 \pi}{3}\right)\) (June 2015)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 20

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 2.
tan-1\(\left(\tan \frac{3 \pi}{4}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 21

Question 3.
cos-1\(\left(\cos \frac{7 \pi}{6}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 22

Question 4.
sin-1\(\left(\sin \frac{3 \pi}{5}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 23

Question 5.
tan-1 √3 – sec-1 (-2).
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 24

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 6.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 25
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 26

Question 7.
tan\(\left(\sin ^{-1} \frac{3}{5}+\cot ^{-1} \frac{3}{2}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 27

Question 8.
tan-1\(\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 28

Question 9.
If sin \(\left\{\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right\}\) = 1, find x.
Answer:
2nd PUC Maths Question Bank Chapter - 2I nverse Trigonometric Functions - 29

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 10.
Evaluate sin-1[sin(-600°)]]
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 30

Question 11.
Evaluate tan(cos-1\(\frac { 3 }{ 5 }\) + tan-1\(\frac { 1 }{ 4 }\))
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 31
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 32

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 12.
Evaluate sin[2 sin-1 0.6]
Answer:
Let sin-1(0.6) = θ ⇒ sin θ = 0.6
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 33
sin 2θ = 2 sinθ cosθ = 2(0.6)(0.8) = 0.96
∴ sin[2sin-1 (0.6)] = 0.96

Question 13.
If sin-1 x + sin-1 y = then find the value of cos-1 x + cos-1 y.
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 34

Question 14.
Find the domain of cos-1 (x2 – 4)
Answer:
cos-1 (x2 – 4) = θ
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 35

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 15.
Find the domain of sin-1(-x2).
Answer:
Let sin-1(-x2) = θ
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 36

Question 16.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 37
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 38

Question 17.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 39
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 40

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 18.
Evaluate tan-1\(\left[\tan \frac{9 \pi}{8}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 41

Question 19.
Evaluate cos-1[cos(-680)]
Answer:
cos-1 [cos (-680)] = cos-1 [cos (680)] .
cos-1 [cos (720 – 40)] = cos-1 [cos(-40)] = cos-1 [cos 40] = 40 = \(\frac{2 \pi}{9}\)

Question 20.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 42
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 43

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 21.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 44
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 45

Question 22.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 46
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 47

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 23.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 48
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 49

Question 24.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 50
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 51

Question 25.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 52
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 53

Question 26.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 54
Answer:
Let x = a sin θ ⇒ θ = sin-1 \(\frac{x}{a}\)
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 55

Question 27.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 56
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 57

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 28.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 58
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 59

Question 29.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 60
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 61

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

2nd PUC Maths Inverse Trigonometric Functions Three Marks Questions With Answers

Question 1.
Prove that tan-1x + tan-1y = tan-1\(\left(\frac{x+y}{1-x y}\right)\) when xy < 1.
Answer:
Let tan-1x = α ⇒ tan α = x
tan-1y = β ⇒ tan β = y
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 62

Question 2.
Prove that tan-1x – tan-1y = tan-1\(\left(\frac{x-y}{1+x y}\right)\), xy > – 1.
Answer:
Let tan-1x = α ⇒ tan α = x
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 63

Question 3.
Prove that 2 tan-1\(\frac { 1 }{ 2 }\) + tan-1\(\frac { 1 }{ 7 }\) = tan-1\(\frac { 31 }{ 17 }\).
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 64
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 65

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 4.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 66
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 67

Question 5.
Solve tan-12x + tan-13x = \(\frac{\pi}{4}\)
Answer:
tan-12x + tan-13x = \(\frac{\pi}{4}\)
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 68
⇒ \(\frac{5 x}{1-6 x^{2}}\) = 1 ⇒ 5x = 1 – 6x2 ⇒ 6x2 + 5x – 1 = 0 ⇒ x = -1 or x = \(\frac{1}{6}\)
Since x = -1 does not saisíy the equation, x = \(\frac{1}{6}\) is the only solution of the given equation.

Question 6.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 69
Answer:
Let x = tan θ ⇒ θ = tan-1x
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 70
= tan-1(tan 3θ) = 3θ = 3 tan-1x = tan-1x + 2tan-1x
= tan-1x + tan-1\(\frac{2 x}{1-x^{2}}\) = LHS.

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 7.
Show that sin-1\(\frac { 3 }{ 5 }\) – sin-1\(\frac { 8 }{ 17 }\) = cos-1\(\frac { 84 }{ 85 }\).
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 71

Question 8.
Show that sin-1\(\frac { 12 }{ 13 }\) + cos-1\(\frac { 4 }{ 5 }\) + tan-1\(\frac { 63 }{ 16 }\) = π
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 72
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 73

Question 9.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 74
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 75

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 10.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 76
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 77

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 11.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 78
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 79
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 80

Question 12.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 81
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 82

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 13.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 83
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 84
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 85

Question 14.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 86
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 87

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 15.
2 sin-1\(\left(\frac{3}{5}\right)\) = tan-1\(\left(\frac{24}{7}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 88
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 89

Question 16.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 90
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 91

Question 17.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 92
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 93
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 94

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 18.
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 95
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 96

Question 19.
Solve for x
2 tan-1 (cot x) = tan-1 (2 cosec x)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 97

2nd PUC Maths Question Bank Chapter 2 Inverse Trigonometric Functions

Question 20.
Solve for x : tan-1 \(\left(\frac{1-x}{1+x}\right)=\frac{1}{2}\) tan-1x (x > 0)
Answer:
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 98
2nd PUC Maths Question Bank Chapter - 2 Inverse Trigonometric Functions - 99

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