NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1 Trigonometric Functions in English as well as in Hindi free to use and download.

NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

Section Name	Topic Name
3.1	Introduction
3.2	Angles
3.3	Trigonometric Functions
3.4	Trigonometric Functions of Sum and Difference of Two Angles
3.5	Trigonometric Equations
3.6	Summary

NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1

Ex 3.1 Class 11 Question 1:
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Ex 3.1 Class 11 Question 2:
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Clik here to view. कक्षा ११ के अध्याय ३ त्रिकोणमितीय फलन की प्रशनावली ३.१
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More Resources for CBSE Class 11

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Ex 3.1 Class 11 Question 6:
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Ex 3.1 Class 11 Question 7:
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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2

Ex 3.2 Class 11 Question 1:
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Clik here to view. 11 Maths Chapter 3 Exercise 3.3 solutions in English
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Ex 3.2 Class 11 Question 2:
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Ex 3.2 Class 11 Question 4:
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Ex 3.2 Class 11 Question 5:
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Ex 3.2 Class 11 Question 6:
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Ex 3.2 Class 11 Question 7:
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Ex 3.2 Class 11 Question 8:
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Ex 3.2 Class 11 Question 9:
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Ex 3.2 Class 11 Question 10:
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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.3

Ex 3.3 Class 11 Question 1:

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Ex 3.3 Class 11 Question 2:
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Ex 3.3 Class 11 Question 3:
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Ex 3.3 Class 11 Question 4:
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Ex 3.3 Class 11 Question 5:
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Ex 3.3 Class 11 Question 6:
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Ex 3.3 Class 11 Question 7:
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Ex 3.3 Class 11 Question 8:
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Ex 3.3 Class 11 Question 9:
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Ex 3.3 Class 11 Question 10:
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Ex 3.3 Class 11 Question 11:
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Ex 3.3 Class 11 Question 12:
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Ex 3.3 Class 11 Question 13:
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Ex 3.3 Class 11 Question 14:
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Ex 3.3 Class 11 Question 15:
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Ex 3.3 Class 11 Question 16:
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Ex 3.3 Class 11 Question 17:
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Ex 3.3 Class 11 Question 18:
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Ex 3.3 Class 11 Question 19:
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Ex 3.3 Class 11 Question 20:
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Ex 3.3 Class 11 Question 21:
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Ex 3.3 Class 11 Question 22:
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Ex 3.3 Class 11 Question 23:
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11 Maths Chapter 3 Exercise 3.3 Question 24:
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11 Maths Chapter 3 Exercise 3.3 Question 25:
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Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.4

Trigonometric Functions class 11 Ex 3.4 Question 1:
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Trigonometric Functions class 11 Ex 3.4 Question 2:
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Trigonometric Functions class 11 Ex 3.4 Question 3:
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Trigonometric Functions class 11 Ex 3.4 Question 4:
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Trigonometric Functions class 11 Ex 3.4 Question 5:
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Trigonometric Functions class 11 Ex 3.4 Question 6:
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Trigonometric Functions class 11 Ex 3.4 Question 7:
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Trigonometric Functions class 11 Ex 3.4 Question 8:
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Trigonometric Functions class 11 Ex 3.4 Question 9:
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NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

Miscellaneous Exercise chapter 3 class 11 Question 1:
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Miscellaneous Exercise chapter 3 class 11 Question 2:
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Miscellaneous Exercise chapter 3 class 11 Question 3:

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Miscellaneous Exercise chapter 3 class 11 Question 4:
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Miscellaneous Exercise chapter 3 class 11 Question 5:
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Miscellaneous Exercise chapter 3 class 11 Question 6:
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Miscellaneous Exercise chapter 3 class 11 Question 7:
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Miscellaneous Exercise chapter 3 class 11 Question 8:
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Miscellaneous Exercise chapter 3 class 11 Question 9:
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Miscellaneous Exercise chapter 3 class 11 Question 10:
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Exercise 3.1

Q.1: Calculate the radian measurement of the given degree measurement:

(i). 25∘

(ii). 240∘

(iii). −47∘30‘

(iv). 520∘

Q.2: Calculate the degree measurement of the given degree measurement: [Use π = Image may be NSFW.
Clik here to view. $\\ \frac { 22 }{ 7 }$ ]

(i) Image may be NSFW.
Clik here to view. $\\ \frac { 11 }{ 16 }$

(ii) -4

(iii) Image may be NSFW.
Clik here to view. $\frac { 5\pi }{ 3 }$

(iv) Image may be NSFW.
Clik here to view. $\frac { 7\pi }{ 6 }$

Q.3: In a minute, wheel makes 360 revolutions. Through how many radians does it turn in 1 second?

Q.4: Calculate the degree measurement of the angle subtended at the centre of a circle of radius 100 m by an arc of length 22 m.

Q.5: In a circle of diameter 40 m, the length of the chord 20 m. Find the length of minor arc of chord.

Q.6: In two circles, arcs which has same length subtended at an angle of 60∘ and 75∘ at the center. Calculate the ratio of their radii.

Q.7: Calculate the angle in radian through which a pendulum swings if the length is 75 cm and the tip describes an arc of length

(i) 10 cm

(ii) 15 cm

(iii) 21 cm

Exercise 3.2

Q.1: Calculate the values of five trigonometric func. if cosy = Image may be NSFW.
Clik here to view. $- \frac { 1 }{ 2 }$ and y lies in 3^rd quadrant.

(i) sec y

(ii) sin y

(iii) cosec y

(iv) tan y

(v) cot y

Q.2: Calculate the other five trigonometric function if we are given the values for sin y = Image may be NSFW.
Clik here to view. $\\ \frac { 3 }{ 5 }$ , where y lies in second quadrant.

Q.3: Find the values of other five trigonometric functions if coty=Image may be NSFW.
Clik here to view. $\\ \frac { 3 }{ 4 }$ , where y lies in the third quadrant.

Q.4: Find the values of other five trigonometric if secy=Image may be NSFW.
Clik here to view. $\\ \frac { 13 }{ 5 }$ , where y lies in the fourth quadrant.

Q.5: Find the values of other five trigonometric function if tan y = Image may be NSFW.
Clik here to view. $- \frac { 5 }{ 12 }$ and y lies in second quadrant.

Q.6: Calculate the value of trigonometric function sin 765°.

Q.7: Calculate the value of trigonometric function cosec [-1410°]

Q.8: Calculate the value of the trigonometric function tan Image may be NSFW.
Clik here to view. $\frac { 19\pi }{ 3 }$ .

Q.9: Calculate the value of the trigonometric function sin Image may be NSFW.
Clik here to view. $-\frac { 11\pi }{ 3 }$ .

Q.10: Calculate the value of the trigonometric function cot Image may be NSFW.
Clik here to view. $-\frac { 15\pi }{ 4 }$

Exercise 3.3

Q.1: Prove:

sin²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 6 }$ +cos²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 3 }$ –tan²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 4 }$ = Image may be NSFW.
Clik here to view. $- \frac { 1 }{ 2 }$

Q.2: Prove:

2sin²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 6 }$ +cosec²Image may be NSFW.
Clik here to view. $\frac { 7\pi }{ 6 }$ 6cos²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 3 }$ =Image may be NSFW.
Clik here to view. $\\ \frac { 3 }{ 2 }$

Q.3: Prove:

cot²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 6 }$ +cosecImage may be NSFW.
Clik here to view. $\frac { 5\pi }{ 6 }$ +3tan²latex s=2]\frac { \pi }{ 6 } [/latex]=6

Q.4: Prove:

2sin²Image may be NSFW.
Clik here to view. $\frac { 3\pi }{ 4 }$ +2cos²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 4 }$ +2sec²Image may be NSFW.
Clik here to view. $\frac { \pi }{ 3 }$ =10

Q.5: Calculate the value of:

(i). sin75∘

(ii). tan15∘

Q.6:Prove:

cos(Image may be NSFW.
Clik here to view. $\frac { \pi }{ 4 }$ –x)cos(Image may be NSFW.
Clik here to view. $\frac { \pi }{ 4 }$ –y)–sin(Image may be NSFW.
Clik here to view. $\frac { \pi }{ 4 }$ –x)sin(Image may be NSFW.
Clik here to view. $\frac { \pi }{ 4 }$ –y)=sin(x+y)

Q.7: Prove:

Image may be NSFW.
Clik here to view. $\frac { tan(\frac { \pi }{ 4 } +x) }{ tan(\frac { \pi }{ 4 } -x) } ={ \left( \frac { 1+tanx }{ 1-tanx } \right) }^{ 2 }$

Q.8: Prove:

Image may be NSFW.
Clik here to view. $\frac { cos(\pi +x)cos(-x) }{ sin(\pi -x)cos\left( \frac { \pi }{ 2 } +x \right) } ={ cot }^{ 2 }x$

Q.9: Prove:

Image may be NSFW.
Clik here to view. $cos(\frac { 3\pi }{ 2 } +x)cos(2\pi +x)[cot(\frac { 3\pi }{ 2 } -x)+cot(2\pi +x)]=1$

Q.10: Prove:

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

Q.11 Prove:

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Clik here to view. $cos(\frac { 3\pi }{ 4 } +x)-cos(\frac { 3\pi }{ 4 } -x)$ =−√2sinx

Q.12: Prove:

sin²6x–sin²4x=sin2x sin10x

Q.13: Prove:

cos²2x–cos²6x=sin4x sin8x

Q.14:Prove:

sin2x+2sin4x+sin6x=4cos²x sin4x

Q.15: Prove:

cot4x(sin5x+sin3x)=cotx(sin5x–sin3x)

Q.16: Prove:

Image may be NSFW.
Clik here to view. $\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x }$

Q.17: Prove:

Image may be NSFW.
Clik here to view. $\frac { sin5x+sin3x }{ cos5x+cos3x } =tan4x$

Q.18: Prove:

Image may be NSFW.
Clik here to view. $\frac { sinx-siny }{ cosx+cosy } =tan\frac { x-y }{ 2 }$

Q.19: Prove:

Image may be NSFW.
Clik here to view. $\frac { sinx+sin3x }{ cosx+cos3x } =tan2x$

Q.20: Prove:

Image may be NSFW.
Clik here to view. $\frac { sinx-sin3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } =2sinx$

Q.21: Prove:

Image may be NSFW.
Clik here to view. $\frac { cos4x+cos3x+cos2x }{ sin4x+sin3x+sin2x } =cot3x$

Q.22: Prove:

cotxcot2x–cot2xcot3x–cot3xcotx=1

Q.23: Prove:

Image may be NSFW.
Clik here to view. $tan4x=\frac { 4tanx(1-{ tan }^{ 2 }x) }{ 1-6{ tan }^{ 2 }x+{ tan }^{ 4 }x }$

Q.24: Prove:

cos4x=1–8sin²xcos²x

Q.25: Prove:

cos6x=32cos⁶x–48cos⁴x+18cos²x−1

Exercise 3.4

Q.1: Find general solutions and the principle solutions of the given equation: tan x = √3

Q.2: Find general solutions and the principle solutions of the given equation: sec x = 2

Q.3: Find general solutions and the principle solutions of the given equation: cot = −√3

Q.4: Find general solutions and the principle solutions of the given equation: cosec x = -2

Q.5: Find the general solution of the given equation: cos 4x = cos 2x

Q.6: Find the general solution of the given equation: cos 3x + cos x – cos 2x = 0

Q.7: Find the general solution of the given equation: sin 2x + cos x = 0

Q.8: Find the general solution of the given equation: sec²2x=1–tan2x

Q.9: Find the general solution of the given equation: sin x + sin 3x + sin 5x = 0

Miscellaneous Exercise

Q.1: Prove that:

Image may be NSFW.
Clik here to view. $2cos\frac { \pi }{ 13 } cos\frac { 9\pi }{ 13 } +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 } =0$

Q.2: Prove that:

(sin3x+sinx)sinx+(cos3x–cosx)cosx=0

Q-3: Prove that:

(cosx+cosy)²+(sinx–siny)²=4cos²Image may be NSFW.
Clik here to view. $\\ \frac { x+y }{ 2 }$

Q-4: Prove that:

(cosx–cosy)²+(sinx–siny)²=4sin²Image may be NSFW.
Clik here to view. $\\ \frac { x-y }{ 2 }$

Q-5: Prove that:

sinx+sin3x+sin5x+sin7x=4cosxcos2xcos4x

Q-6: Prove that:

Image may be NSFW.
Clik here to view. $\frac { (sin7x+sin5x)+(sin9x+sin3x) }{ (cos7x+cos5x)+(cos9x+cos3x) } =tan6x$

Q-7: Show that: sin3y+sin2y–siny=4sinycosImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ cosImage may be NSFW.
Clik here to view. $\\ \frac { 3y }{ 2 }$

Q-8: The value of tany=Image may be NSFW.
Clik here to view. $- \frac { 4 }{ 2 }$ where y in in 2^nd quadrant then find out the values of sinImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ ,cosImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ and tanImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ .

Q-9: The value of cosy=Image may be NSFW.
Clik here to view. $- \frac { 1 }{ 3 }$ where y in in 3^rd quadrant then find out the values of sinImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ ,cosImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ and tanImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ .

Q-10: The value of siny=Image may be NSFW.
Clik here to view. $\\ \frac { 1 }{ 4 }$ where y in in 2^nd quadrant then find out the values of sinImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ ,cosImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ and tanImage may be NSFW.
Clik here to view. $\\ \frac { y }{ 2 }$ .

NCERT Solutions for Class 11 Maths All Chapters

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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions