NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions – in hindi

Maths Class 12 NCERT Solutions Chapter 2 Exercises
Exercise 2.1
Exercise 2.2
Miscellaneous Exercise

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 4UP 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

I 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 14.1UP 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-

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 15.1UP 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 17.1UP 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

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