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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 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 2

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

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

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 4.1

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 5

प्रश्न 6.
tan-1(-1) का मुख्य मान ज्ञात कीजिए।


हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 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 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 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 9

प्रश्न 10.
cosec-1 (-√2) का मुख्य मान ज्ञात कीजिए।
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 10

प्रश्न 11.


UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 11 का मान ज्ञात कीजिए।


हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 11.1

प्रश्न 12.


UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 12 का मान ज्ञात कीजिए।
हल

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 12.1

प्रश्न 13.
यदि sin-1 x = y, तो
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 13
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 13.1

प्रश्न 14.
tan-1√3 – sec-1(-2) का मान बराबर है


UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 14
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 14.1
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 14.2

——————————————————

प्रश्नावली 2.2

निम्नलिखित को सिद्ध कीजिए–

प्रश्न 1.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 1
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 2
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 3
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 3.1

प्रश्न 4.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 4
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 4.1

निम्नलिखित फलनों को सरलतम रूप में लिखिए

प्रश्न 5.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 5

हल

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 5.1

प्रश्न 6.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 6
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 6.1

प्रश्न 7.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 7
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 7.1

प्रश्न 8.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 8
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 8.1

प्रश्न 9.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 9
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 9.1

प्रश्न 10.

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 10


हल

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 10.1

प्रश्न 11.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 11
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 11.1

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 12

प्रश्न 13.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 13
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 13.1

प्रश्न 14.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 14
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 14.1

प्रश्न 15.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 15
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 15.1
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 15.2

प्रश्न 16.
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 16
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 16.1

प्रश्न 17.

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 17


हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 17.1
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 17.2

प्रश्न 18.

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 18

हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 18.1

प्रश्न 19.


UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 19
हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 19.1

प्रश्न 20.

UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 20

हल
UP Board Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions 20.1

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 21

Chapter 2 Inverse Trigonometric Functions hindi