Class 12th maths notes chapter 2 Inverse trigonometric function Ex 2.2

Class 12th maths notes chapter 2 Inverse trigonometric function Ex 2.2

Mp board class 12th maths book solution chapter 2 Inverse trigonometric function pdf साझा की हैं, ये हल 12वीं गणित के छात्रों के लिए अति महत्वपूर्ण है। ये समाधान नवीनतम एमपी बोर्ड पुस्तकों के विषय विशेषज्ञों द्वारा हल किए गए हैं।  MP Board Class 12th Maths Solutions Chapter 2 प्रतिलोम त्रिकोणमितीय फलन Ex 2.2

इस लेख में, हमने  MP board class 12th maths book solution chapter 2 Inverse trigonometric function pdf साझा की हैं, ये हल 12वीं गणित के छात्रों के लिए अति महत्वपूर्ण है। ये समाधान नवीनतम एमपी बोर्ड पुस्तकों के विषय विशेषज्ञों द्वारा हल किए गए हैं।

MP Board Class 12th Maths Solutions Chapter 2 प्रतिलोम त्रिकोणमितीय फलन Ex 2.2 

यहाँ पर 12वीं गणित अध्याय 2 प्रतिलोम त्रिकोणमितीय फलन का अभ्यास 2.2 का हल प्रस्तुत कर रहे हैं। जो कि आगे आने वाली अभ्यासों का आधार बनायेगा। आइये शुरू करते हैं।

निम्नलिखित को सिद्ध कीजिए-
प्रश्न 1.
3 sin-1 x = sin-1(3x – 4x3), x ϵ [12,12]

हल:
माना sin-1x = y
⇒ x = sin y
R.H.S. = sin-1 (3x – 4x3)
= sin-1(3 sin y – 4 sin3 y)
= sin-1 (sin 3y)
(∵ sin 3y = 3 sin y – 4 sin3y)
= 3y (∵ sin-1 sin x = x)
= 3 sin-1 x
= L.H.S.
अत: 3 sin-1x = sin-1(3x – 4x3)


प्रश्न 2.
3 cos-1 x = cos-1 (4x3 – 3x), x ϵ [12,1]
हल:
सिद्ध करना है
3cos-1 x = cos-1 (4x3 – 3x) …(1)
माना cos-1 = y
⇒ x = cosy
∴ समी० (1) का RH.S.
=cos-1(4x3 – 3x)
= cos-1 (4cos3 y – 3cos y)
=cos-1 (cos 3y)
= 3y
= 3cos-1x (∵ cos-1 x = y)
अत: 3cos-1 = cos-1 (4x3 – 3x)


प्रश्न 3.
tan-1211 + tan-1724 = tan-112
हल:
हम जानते हैं कि

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प्रश्न 4.
2 tan-112 + tan-117 = tan-13117
हल:
2 tan-112 + tan-117 = tan-13117

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निम्नलिखित फलनों को सरलतम रूप में लिखिए-
प्रश्न 5.
tan-1 1+x21x, x ≠ 0
हल:
माना x = tan θ ⇒ θ = tan-1x

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प्रश्न 6.
tan-11x21, |x| > 1.
हल:
माना x = secθ ⇒ θ = sec-1x

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प्रश्न 7.
tan-1(1cosx1+cosx), 0 < x < π
हल:

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प्रश्न 8.
tan-1(cosxsinxcosx+sinx),π4<x<3π4
हल:

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प्रश्न 9.
tan-1xa2x2, |x| < a
हल:
माना x = a sin θ ⇒ xa = sin θ

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प्रश्न 10.

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हल: 

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निम्नलिखित में से प्रत्येक का मान ज्ञात कीजिए
प्रश्न 11.
tan-1[2cos (2sin-112)]
हल:

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प्रश्न 12.
cot (tan-1 a + cot-1 a)
हल:
माना y = cot (tan-1a + cot-1a)
= cotπ2 [∵ tan-1a + cot-1a = π2]
= 0 [∵ cot π2 = 0]


प्रश्न 13.

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प्रश्न 14.
यदि sin(sin-115 + cos-1x) = 1, तो x का मान ज्ञात कीजिए।
हल

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प्रश्न 15.
यदि tan-1 x1x2 + tan-1x+1x+2=π4, तो x का मान ज्ञात कीजिए।
हल:
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प्रश्न संख्या 16 से 18 में दिए गए प्रत्येक व्यंजक का मान ज्ञात कीजिए-
प्रश्न 16.
sin-1 (sin2π3)
हल

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प्रश्न 17.
tan-1 (tan3π4)
हल

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प्रश्न 18.
tan (sin-135 + cot-132)
हल: 

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प्रश्न 19.
cos-1(cos 7π6) का मान बराबर है-

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प्रश्न 20.
sin [π3 – sin-1(12)] का मान है-

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प्रश्न 21.
tan-13 – cot-1 (-3) का मान है
(A) π
(B) π2
(C) 0
(D) 2

3
हल:

MP Board Class 12th Maths Solutions Chapter 2 प्रतिलोम त्रिकोणमितीय फलन


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