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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ch 3 class 11 maths NCERT Solutions
11 Maths Chapter 3 Exercise 3.1
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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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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2 for up board and cbse
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११ गणित प्रशनावली ३.२ के हिंदी मीडियम ke hal
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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2

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NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.3

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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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NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

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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 = $\\ \frac { 22 }{ 7 }$ ]

(i) $\\ \frac { 11 }{ 16 }$

(ii) -4

(iii) $\frac { 5\pi }{ 3 }$

(iv) $\frac { 7\pi }{ 6 }$

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 = $- \frac { 1 }{ 2 }$ 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 = $\\ \frac { 3 }{ 5 }$ , where y lies in second quadrant.

Q.3: Find the values of other five trigonometric functions if coty= $\\ \frac { 3 }{ 4 }$ , where y lies in the third quadrant.

Q.4: Find the values of other five trigonometric if secy= $\\ \frac { 13 }{ 5 }$ , where y lies in the fourth quadrant.

Q.5: Find the values of other five trigonometric function if tan y = $- \frac { 5 }{ 12 }$ 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 $\frac { 19\pi }{ 3 }$ .

Q.9: Calculate the value of the trigonometric function sin $-\frac { 11\pi }{ 3 }$ .

Q.10: Calculate the value of the trigonometric function cot $-\frac { 15\pi }{ 4 }$

Exercise 3.3

Q.1: Prove:

sin² $\frac { \pi }{ 6 }$ +cos² $\frac { \pi }{ 3 }$ –tan² $\frac { \pi }{ 4 }$ = $- \frac { 1 }{ 2 }$

Q.2: Prove:

2sin² $\frac { \pi }{ 6 }$ +cosec² $\frac { 7\pi }{ 6 }$ 6cos² $\frac { \pi }{ 3 }$ = $\\ \frac { 3 }{ 2 }$

Q.3: Prove:

cot² $\frac { \pi }{ 6 }$ +cosec $\frac { 5\pi }{ 6 }$ +3tan²latex s=2]\frac { \pi }{ 6 } [/latex]=6

Q.4: Prove:

2sin² $\frac { 3\pi }{ 4 }$ +2cos² $\frac { \pi }{ 4 }$ +2sec² $\frac { \pi }{ 3 }$ =10

Q.5: Calculate the value of:

(i). sin75∘

(ii). tan15∘

Q.6:Prove:

cos( $\frac { \pi }{ 4 }$ –x)cos( $\frac { \pi }{ 4 }$ –y)–sin( $\frac { \pi }{ 4 }$ –x)sin( $\frac { \pi }{ 4 }$ –y)=sin(x+y)

Q.7: Prove:

$\frac { tan(\frac { \pi }{ 4 } +x) }{ tan(\frac { \pi }{ 4 } -x) } ={ \left( \frac { 1+tanx }{ 1-tanx } \right) }^{ 2 }$

Q.8: Prove:

$\frac { cos(\pi +x)cos(-x) }{ sin(\pi -x)cos\left( \frac { \pi }{ 2 } +x \right) } ={ cot }^{ 2 }x$

Q.9: Prove:

$cos(\frac { 3\pi }{ 2 } +x)cos(2\pi +x)[cot(\frac { 3\pi }{ 2 } -x)+cot(2\pi +x)]=1$

Q.10: Prove:

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

Q.11 Prove:

$cos(\frac { 3\pi }{ 4 } +x)-cos(\frac { 3\pi }{ 4 } -x)$ =−√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:

$\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x }$

Q.17: Prove:

$\frac { sin5x+sin3x }{ cos5x+cos3x } =tan4x$

Q.18: Prove:

$\frac { sinx-siny }{ cosx+cosy } =tan\frac { x-y }{ 2 }$

Q.19: Prove:

$\frac { sinx+sin3x }{ cosx+cos3x } =tan2x$

Q.20: Prove:

$\frac { sinx-sin3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } =2sinx$

Q.21: Prove:

$\frac { cos4x+cos3x+cos2x }{ sin4x+sin3x+sin2x } =cot3x$

Q.22: Prove:

cotxcot2x–cot2xcot3x–cot3xcotx=1

Q.23: Prove:

$tan4x=\frac { 4tanx(1-{ tan }^{ 2 }x) }{ 1-6{ tan }^{ 2 }x+{ tan }^{ 4 }x }$

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:

$2cos\frac { \pi }{ 13 } cos\frac { 9\pi }{ 13 } +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 } =0$

Q.2: Prove that:

(sin3x+sinx)sinx+(cos3x–cosx)cosx=0

Q-3: Prove that:

(cosx+cosy)²+(sinx–siny)²=4cos² $\\ \frac { x+y }{ 2 }$

Q-4: Prove that:

(cosx–cosy)²+(sinx–siny)²=4sin² $\\ \frac { x-y }{ 2 }$

Q-5: Prove that:

sinx+sin3x+sin5x+sin7x=4cosxcos2xcos4x

Q-6: Prove that:

$\frac { (sin7x+sin5x)+(sin9x+sin3x) }{ (cos7x+cos5x)+(cos9x+cos3x) } =tan6x$

Q-7: Show that: sin3y+sin2y–siny=4sinycos $\\ \frac { y }{ 2 }$ cos $\\ \frac { 3y }{ 2 }$

Q-8: The value of tany= $- \frac { 4 }{ 2 }$ where y in in 2^nd quadrant then find out the values of sin $\\ \frac { y }{ 2 }$ ,cos $\\ \frac { y }{ 2 }$ and tan $\\ \frac { y }{ 2 }$ .

Q-9: The value of cosy= $- \frac { 1 }{ 3 }$ where y in in 3^rd quadrant then find out the values of sin $\\ \frac { y }{ 2 }$ ,cos $\\ \frac { y }{ 2 }$ and tan $\\ \frac { y }{ 2 }$ .

Q-10: The value of siny= $\\ \frac { 1 }{ 4 }$ where y in in 2^nd quadrant then find out the values of sin $\\ \frac { y }{ 2 }$ ,cos $\\ \frac { y }{ 2 }$ and tan $\\ \frac { y }{ 2 }$ .

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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions