UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन) are part of UP Board Solutions for Class 12 Maths. Here we have given UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन)

Board UP Board
Textbook NCERT
Class Class 12
Subject Maths
Chapter Chapter 2
Chapter Name Inverse Trigonometric Functions
Exercise Ex 1.1, Ex 1.2
Number of Questions Solved 35
Category UP Board Solutions

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

प्रश्नावली 2.1

प्रश्न 1.
[latex s=2]{ sin }^{ -1 }\left( -\frac { 1 }{ 2 } \right) [/latex] का मुख्य मान ज्ञात कीजिए।
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 1

प्रश्न 2.
[latex s=2]{ cos }^{ -1 }\left( \frac { \sqrt { 3 } }{ 2 } \right) [/latex] का मुख्य मान ज्ञात कीजिए।
हल-
cos-1 की मुख्य मान शाखा परिसर [0, π] है।
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 2

UP Board Solutions

प्रश्न 3.
cosec-1 (2) का मुख्य मान ज्ञात कीजिए।
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 3

प्रश्न 4.
tan-1 (-√3) का मुख्य मान ज्ञात कीजिए।
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 4

प्रश्न 5.
[latex s=2]{ cos }^{ -1 }\left( -\frac { 1 }{ 2 } \right) [/latex] का मुख्य मान ज्ञात कीजिए।
हल-
cos-1 की मुख्य मान शाखा परिसर [0, π] है।
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 6

प्रश्न 6.
tan-1(-1) का मुख्य मान ज्ञात कीजिए।
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 6

प्रश्न 7.
[latex s=2]{ sec }^{ -1 }\left( \frac { 2 }{ \sqrt { 3 } } \right) [/latex] का मुख्य मान ज्ञात कीजिए।
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 7

प्रश्न 8.
cot-1(√3) का मुख्य मान ज्ञात कीजिए।
हल-
cot-1 का मुख्य मान शाखा परिसर (0, π) है।
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 8

प्रश्न 9.
[latex s=2]cos^{ -1 }\left( \frac { -1 }{ \sqrt { 2 } } \right) [/latex] का मान ज्ञात कीजिए।
हल-
cos-1 का मुख्य मान शाखा परिसर [0, π] है।
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 9

प्रश्न 10.
cosec-1 (-√2) का मुख्य मान ज्ञात कीजिए।
हल-

UP Board Solutions

प्रश्न 11.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 10
का मान ज्ञात कीजिए।
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 11

प्रश्न 12.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 12
का मान ज्ञात कीजिए।
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 13

प्रश्न 13.
यदि sin-1 x = y, तो
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 14
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 15

प्रश्न 14.
tan-1√3 – sec-1(-2) का मान बराबर है
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 16
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 17
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 18a

प्रश्नावली 2.2

निम्नलिखित को सिद्ध कीजिए–

प्रश्न 1.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 18
हल-
माना sin-1x = θ ∴ sin θ = x
पुनः sin 3θ = 3 sin3 θ – 4 sin० θ
⇒ sin 3θ = 3x – 4x3
⇒ 3θ = sin-1(3x – 4x3)
∴ 3sin-1x = sin-1(3x – 4x3) इति सिद्धम्

प्रश्न 2.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 19
हल-
माना cos-1 x = θ ∴ cosθ = x
∴ cos 3θ = 4cos3θ – 3 cos θ
⇒ cos 3θ = 4x3 – 3x
⇒ 3θ = cos-1(4x3 – 3x)
∴ 3cos-1x = cos-1(4x3 – 3x) इति सिद्धम्

प्रश्न 3.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 20
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 21

प्रश्न 4.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 22
हल-
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निम्नलिखित फलनों को सरलतम रूप में लिखिए

प्रश्न 5.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 24
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 25

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 26
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 27

प्रश्न 7.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 28
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 29

प्रश्न 8.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 30
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 30a

प्रश्न 9.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 31
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 32

UP Board Solutions

प्रश्न 10.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 33
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 34

प्रश्न 11.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 35
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 36

प्रश्न 12.
cot (tan-1 a + cot-1 a)
हल-
माना y = cot (tan-1 a + cot-1 a)
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 37

प्रश्न 13.
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हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 39

प्रश्न 14.
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हल-
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प्रश्न 15.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 43
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 44
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 45
प्रश्न 16.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 46
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 47

प्रश्न 17.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 48
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 49

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 50

प्रश्न 18.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 51
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 52

प्रश्न 19.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 53
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 54

प्रश्न 20.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 55
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 56

प्रश्न 21.
tan-1√3 – cot-1(-√3) का मान है
(A) π
(B) [latex]-\frac { \pi }{ 2 } [/latex]
(C) 0
(D) 2√3
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 57

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