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RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

June 7, 2019 by Prasanna Leave a Comment

Rajasthan Board RBSE Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

सिद्ध कीजिए

प्रश्न 1.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल
प्रश्नानुसार L.H.S.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 2.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 3.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 4.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 5.
मान ज्ञात कीजिया
(i) sin 75°
(ii) tan 15°
हल :
(i) ∵ sin 75°
= sin (45° + 30°)
= sin 45°. cos 30° + cos 45°. sin 30°
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

(ii) tan 15°
= tan (45° – 30°)
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 6.
सिद्ध कीजिए
tan 225° cot 405° + tan 765° cot 675° = 0
हल :
L.H.S. tan 225° cot 405° + tan 765° cot 675°
⇒ tan(180° + 459) cot(360° + 459) + tan(2 x 360° + 45°). cot (2 x 360° – 45°)
⇒ tan 45° cot 45° + tan 45o ° x (-cot 45°)
⇒ tan 45° . cot 45° – tan 45° . cot 45° + 0
= RHS
LHS = RHS

प्रश्न 7.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 8.
निम्नलिखित को सिद्ध कीजिए
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 9.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 10.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 11.
sin (n + 1) x sin (n + 2) x + cos (n + 1) x cos (n + 2) x = cos x
हल :
L.H.S. = sin (n + 1) x sin (n + 2) x + cos (n + 1) x cos (n + 2) x
माना कि (n +1) x = A तथा (n + 2)x = B
= sin A . sin B + cos A cos B
= cos (A – B)
A तथा B का मान रखने पर
= cos [(n + 1)x – (n + 2)x]
= cos (nx + x – nx – 2x]
= cos (x – 2x) = cos (-x)
हम जानते हैं कि cos (-θ) = cos θ ∀θ∈R
= cos x
= R.H.S.

प्रश्न 12.
sin² 6x – sin² 4x = sin 2x sin 10x
हल :
L.H.S. = sin² 6x – sin² 4x
= (sin 6x + sin 4x) (sin 6x – sin 4x)
[∵ a² – b² = (a + b) (a – b)]
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
= (2 sin 5x cos x) (2 cos 5x . sin x)
= (2 sin 5x cos 5x) (2 sin x cos x)
= sin 10x . sin 2x (∵ 2 sin cos θ = sin 2θ)
= R.H.S.
IInd Method :
L.H.S.= sin²6x – sin²4x
= sin (6x + 4x) sin (6x – 4x)
[∵ sin²A – sin²B = sin(A + B) sin(A – B)]
= sin 10x sin 2x
= R.H.S.

प्रश्न 13.
sin 2x + 2 sin 4x + sin 6x = 4 cos² x sin 4x
हल :
L.H.S. = sin 2x + 2 sin 4x + sin 6x
= (sin 2x + sin 6x) + 2 sin 4x
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
= 2 sin (4x) cos (-2x) + 2 sin 4x
= 2 sin 4x (cos 2x + 1)
[∵ cos (-x) = cos x ∀ x ∈ R].
= 2 sin 4x (2 cos²x)
[∵ cos 2x = 2 cos²x – 1]
= 4 cos² x sin 4x
= R.H.S.

प्रश्न 14.
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
हल :
L.H.S. = cot 4x (sin 5x + sin 3x)
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 15.
सिद्ध कीजिए
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 16.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 17.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 18.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 19.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

प्रश्न 20.
cos 4x = 1 – 8sin² x cos² x
हल :
L.H.S.= cos 4x = 1 – 2 sin² 2x = 1 – 2[sin 2x]²
= 1 – 2[2 sin x cos x]²
= 1 – 2[4 sin² x cos² x]
= 1 – 8sin² x cos² x
= R.H.S.

प्रश्न 21.
cos 6x = 32 cos6 x – 48 cos4 + x + 18 cos2 x – 1
हल :
L.H.S. = cos 6x = cos 2(3x)
= 2 cos² 3x – 1
= 2 (4 cos³ x – 3 cos x)² – 1
∵ cos 3x = (4 cos³x – 3 cos x)
= 2 [16 cos6 x – 2 (4 cos3 x) (3 cos x) + 9 cos2 x] – 1
= 2 (16 cos6 x – 24 cos4 x + 9 cos2 x) – 1
= 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
= R.H.S.

प्रश्न 22.
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3
हल :
RBSE Solutions for Class 11 Maths Chapter 3 त्रिकोणमितीय फलन Ex 3.3

RBSE Solutions for Class 11 Maths

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