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RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

June 10, 2019 by Prasanna Leave a Comment

Rajasthan Board RBSE Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

निम्नलिखित समीकरणों के मुख्य तथा व्यापक हल ज्ञात कीजिए

प्रश्न 1.
tan x = √3
हल :
प्रश्नानुसार tan x = √3
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

प्रश्न 2.
sec x = 2
हल :
प्रश्नानुसार sec x = 2
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

प्रश्न 3.
cot x = -√3
हल :
प्रश्नानुसार cot x = -√3
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

प्रश्न 4.
cosec x = – 2
हल :
प्रश्नानुसार cosec x = – 2
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

निम्नलिखित समीकरणों के व्यापक हल ज्ञात कीजिए

प्रश्न 5.
cos 4x = cos 2x
हल :
प्रश्नानुसार cos 4x = cos 2x
या 4x = 2nπ ± 2x
धनात्मक चिह लेने पर 4x = 2nπ + 2x
या 4x – 2x = 2nπ
या 2x = 2nπ
या x = nπ, n ∈ I
ॠणात्मक चिह लेने पर 4x = 2nπ – 2x
4x + 2x = 2nπ
6x = 2nπ
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

प्रश्न 6.
cos 3x + cos x – cos 2x = 0
हल :
प्रश्नानुसार cos 3x + cos x – cos 2x = 0
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

प्रश्न 7.
sin 2x + cos x = 0
हल :
प्रश्नानुसार sin 2x + cos x = 0
या 2 sin x cos x + cos x = 0
या cos x (2sin x + 1) = 0
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

प्रश्न 8.
sec² 2x = 1 – tan 2x
हल :
प्रश्नानुसार sec²x = 1 – tan 2x
⇒ 1 + tan² 2x = 1 – tan 2x
⇒ tan² 2x + tan 2x = 0
⇒ tan 2x (tan 2x + 1) = 0
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

प्रश्न 9.
sin x + sin 3x + sin 5x = 0
हल :
प्रश्नानुसार sin x + sin 3x + sin 5x = 0
या (sin x + sin 5x) + sin 3x = 0
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4
या 2 sin 3x cos (-2x) + sin 3x = 0
या 2 sin 3x cos 2x + sin 3x = 0
या sin 3x (2 cos 2x + 1) = 0
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.4

RBSE Solutions for Class 11 Maths

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