# NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

### NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1

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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

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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).  4730

(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 3rd 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:

sin²6xsin²4x=sin2sin10x

Q.13: Prove:

cos²2xcos²6x=sin4sin8x

Q.14:Prove:

sin2x+2sin4x+sin6x=4cos²sin4x

Q.15: Prove:

cot4x(sin5x+sin3x)=cotx(sin5xsin3x)

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:

cotxcot2xcot2xcot3xcot3xcotx=1

Q.23: Prove:

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

Q.24: Prove:

cos4x=18sin²xcos²x

Q.25: Prove:

cos6x=32cos6x48cos4x+18cos2x1

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=1tan2x

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+(cos3xcosx)cosx=0

Q-3: Prove that:

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

Q-4: Prove that:

(cosxcosy)²+(sinxsiny)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+sin2ysiny=4sinycos$\\ \frac { y }{ 2 }$cos$\\ \frac { 3y }{ 2 }$

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

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

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

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