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

Free PDF download of UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions provides solutions for all the questions enlisted under the chapter. All questions are solved using step by step approach, solving the questions from the Class 12 Maths for helps in grasping the concepts correctly.

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

प्रश्न 2.
{ cos }^{ -1 }\left( \frac { \sqrt { 3 } }{ 2 } \right) 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.
{ cos }^{ -1 }\left( -\frac { 1 }{ 2 } \right) 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.
{ sec }^{ -1 }\left( \frac { 2 }{ \sqrt { 3 } } \right) 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.
cos^{ -1 }\left( \frac { -1 }{ \sqrt { 2 } } \right) 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.
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हल-
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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-
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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.
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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-
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प्रश्न 14.
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हल-
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प्रश्न 15.
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हल-
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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-
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UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 50

प्रश्न 18.
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हल-
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प्रश्न 19.
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हल-
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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) -\frac { \pi }{ 2 }
(C) 0
(D) 2√3
हल-
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions image 57

We hope the UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन) help you. If you have any query regarding UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन), drop a comment below and we will get back to you at the earliest.

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