In This Post we are  providing Chapter -3 Trigonometric Fuctions NCERT Solutions for Class 11 Maths which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These  Class 11  Trigonometric Fuctions solutions can be really helpful in the preparation of Board exams and will provide you with in depth detail of the chapter.

 

We have solved every question stepwise so you don’t have to face difficulty in understanding the solutions. It will also give you concepts that are important for overall development of students. Class 11 Maths  Trigonometric Fuctions NCERT Written Solutions  will be useful in higher classes as well because variety of questions related to these concepts can be asked so you must study and understand them properly.

Class 11th Chapter 3 Trigonometric Fuctions | NCERT MATHS SOLUTION |

Ex 3.1 Class 11 Maths Question 1.
Find the radian measures corresponding to the following degree measures:
(i) 25°
(ii) -47°30′
(iii) 240°
(iv) 520°
Solution.
We have, 180° = π Radians
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 1


Ex 3.1 Class 11 Maths Question 2.
Find the degree measures corresponding to the following radian measures \left( Use\quad \pi =\frac { 22 }{ 7 } \right)
(i) \frac { 11 }{ 16 }
(ii) -4
(iii) \frac { 5\pi }{ 3 }
(iv) \frac { 7\pi }{ 6 }
Solution.
We have π Radians = 180°
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 2

 

Ex 3.1 Class 11 Maths Question 3.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second ?
Solution.
Number of revolutions made by wheel in one minute = 360
As we know that, 1 Revolution = 27 π Radians
∴ 360 Revolutions = 720 π Radians
∴ In 1 minute wheel can make = 720 π Radians
⇒ In 60 seconds wheel can make = 720 π Radians
⇒ In 1 second wheel can make
\frac { 720\pi }{ 3 } Radians=12\pi \quad Radians

Ex 3.1 Class 11 Maths Question 4.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm \left( Use\quad \pi =\frac { 22 }{ 7 } \right)
Solution.
Let O be the centre and AB be the arc length of the circle.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 3

Ex 3.1 Class 11 Maths Question 5.
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of Xhe chord.
Solution.
Let AB be the minor arc of the chord.
AB = 20 cm, OA = OB = 20 cm
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 4

Ex 3.1 Class 11 Maths Question 6.
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their, radii.
Solution.
Let r1 r2 and θ1, θ2 be the radii and angles subtended at the centre of two circles respectively.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 5

Ex 3.1 Class 11 Maths Question 7.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
(i) 10 cm
(ii) 15 cm
(iii) 21 cm
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 6

 

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1, drop a comment below and we will get back to you at the earliest.

Find the values of other five trigonometric functions in Exercises 1 to 5.
Ex 3.2 Class 11 Maths Question 1.
\cos { x } =\frac { -1 }{ 2 } , x lies in third quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 1

 

Ex 3.2 Class 11 Maths Question 2.
\sin { x } =\frac { 3 }{ 5 } , x lies in second quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 2

Ex 3.2 Class 11 Maths Question 3.
\cot { x= } \frac { 3 }{ 4 } , xlies in third quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 3

Ex 3.2 Class 11 Maths Question 4.
\sec { x } =\frac { 13 }{ 5 } , x lies in fourth quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 4

Ex 3.2 Class 11 Maths Question 5.
\tan { x } =-\frac { 5 }{ 12 } , x lies in second quadrant.
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 4

Find the values of the trigonometric functions in Exercises 6 to 10.
Ex 3.2 Class 11 Maths Question 6.
sin 765°
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 5

Ex 3.2 Class 11 Maths Question 7.
cosec (-1410°)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 6

Ex 3.2 Class 11 Maths Question 8.
tan\quad \frac { 19\pi }{ 3 }
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 7

Ex 3.2 Class 11 Maths Question 9.
sin\left( -\frac { 11\pi }{ 3 } \right)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 8

Ex 3.2 Class 11 Maths Question 10.
cot\left( -\frac { 15\pi }{ 4 } \right)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 9

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.2, drop a comment below and we will get back to you at the earliest.

Ex 3.3 Class 11 Maths Question 1.
Prove that: { sin }^{ 2 }\frac { \pi }{ 6 } +{ cos }^{ 2 }\frac { \pi }{ 3 } -{ tan }^{ 2 }\frac { \pi }{ 4 } =-\frac { 1 }{ 2 }
Solution.
L.H.S. = { sin }^{ 2 }\frac { \pi }{ 6 } +{ cos }^{ 2 }\frac { \pi }{ 3 } -{ tan }^{ 2 }\frac { \pi }{ 4 } =-\frac { 1 }{ 2 }
=\left[ { \left( \frac { 1 }{ 2 } \right) }^{ 2 }+{ \left( \frac { 1 }{ 2 } \right) }^{ 2 }-{ \left( 1 \right) }^{ 2 } \right] =\frac { 1 }{ 4 } +\frac { 1 }{ 4 } -1=\frac { -1 }{ 2 } =\quad R.H.S.

Ex 3.3 Class 11 Maths Question 2.
2{ sin }^{ 2 }\frac { \pi }{ 6 } +{ cosec }^{ 2 }\frac { 7\pi }{ 6 } { cos }^{ 2 }\frac { \pi }{ 3 } =\frac { 3 }{ 2 }
Solution.
L.H.S. = 2{ sin }^{ 2 }\frac { \pi }{ 6 } +{ cosec }^{ 2 }\frac { 7\pi }{ 6 } { cos }^{ 2 }\frac { \pi }{ 3 }
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 1

Ex 3.3 Class 11 Maths Question 3.
{ cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 } =6
Solution.
L.H.S. = { cot }^{ 2 }\frac { \pi }{ 6 } +cosec\frac { 5\pi }{ 6 } +3{ tan }^{ 2 }\frac { \pi }{ 6 }
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 2

Ex 3.3 Class 11 Maths Question 4.
2{ sin }^{ 2 }\frac { 3\pi }{ 4 } +2{ cos }^{ 2 }\frac { \pi }{ 4 } +2{ sec }^{ 2 }\frac { \pi }{ 3 } =10
Solution.
L.H.S. = 2{ sin }^{ 2 }\frac { 3\pi }{ 4 } +2{ cos }^{ 2 }\frac { \pi }{ 4 } +2{ sec }^{ 2 }\frac { \pi }{ 3 }
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 3

Ex 3.3 Class 11 Maths Question 5.
Find the value of:
(i) sin 75°
(ii) tan 15°
Solution.
(i) sin (75°) = sin (30° + 45°)
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 4

(ii) tan 15° = tan (45° – 30°)
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 5

Prove the following:
Ex 3.3 Class 11 Maths Question 6.
cos\left( \frac { \pi }{ 4 } -x \right) cos\left( \frac { \pi }{ 4 } -y \right) -sin\left( \frac { \pi }{ 4 } -x \right) sin\left( \frac { \pi }{ 4 } -y \right)
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 6

Ex 3.3 Class 11 Maths Question 7.
\frac { tan\left( \frac { \pi }{ 4 } +x \right) }{ tan\left( \frac { \pi }{ 4 } -x \right) } ={ \left( \frac { 1+tan\quad x }{ 1-tan\quad x } \right) }^{ 2 }
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 7

Ex 3.3 Class 11 Maths Question 8.
\frac { cos\left( \pi +x \right) cos\left( -x \right) }{ sin\left( \pi -x \right) cos\left( \frac { \pi }{ 2 } +x \right) } ={ cot }^{ 2 }x
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 8

Ex 3.3 Class 11 Maths Question 9.
cos\left( \frac { 3\pi }{ 2 } +x \right) cos\left( 2\pi +x \right) \left[ cot\left( \frac { 3\pi }{ 2 } -x \right) +cot\left( 2\pi +x \right) \right] =1
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 9

Ex 3.3 Class 11 Maths Question 10.
sin(n +1 )x sin(n + 2)x + cos(n +1 )x cos(n + 2)x = cosx
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 10

Ex 3.3 Class 11 Maths Question 11.
cos\left( \frac { 3\pi }{ 4 } +x \right) -cos\left( \frac { 3\pi }{ 4 } -x \right) =-\sqrt { 2 } sinx
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 11

Ex 3.3 Class 11 Maths Question 12.
sin26x – sin24x= sin2x sin10x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 12

Ex 3.3 Class 11 Maths Question 13.
cos22x – cos26x = sin 4x sin 8x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 13

Ex 3.3 Class 11 Maths Question 14.
sin2x + 2 sin 4x + sin 6x = 4 cos2 x sin 4x
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 14

Ex 3.3 Class 11 Maths Question 15.
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 15

Ex 3.3 Class 11 Maths Question 16.
\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x }
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 16

Ex 3.3 Class 11 Maths Question 17.
\frac { sin5x+sin3x }{ cos5x+cos3x } =tan4x
Solution.
We have,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 17

Ex 3.3 Class 11 Maths Question 18.
\frac { sinx-siny }{ cosx+cosy } =tan\left( \frac { x-y }{ 2 } \right)
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 18

Ex 3.3 Class 11 Maths Question 19.
\frac { sinx+sin3x }{ cosx+cos3x } =tan2x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 19

Ex 3.3 Class 11 Maths Question 20.
\frac { sinx-sin3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } =2sinx
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 20

Ex 3.3 Class 11 Maths Question 21.
\frac { cos4x+cos3x+cos2x }{ sin4x+sin3x+sin2x } =cot3x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 21

Ex 3.3 Class 11 Maths Question 22.
cot x cot 2x – cot 2x cot 3x – cot3x cotx = 1
Solution.
We know that 3x = 2x + x.
Therefore,
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 22

Ex 3.3 Class 11 Maths Question 23.
tan4x=\frac { 4tanx\left( 1-{ tan }^{ 2 }x \right) }{ 1-6{ tan }^{ 2 }x+{ tan }^{ 4 }x }
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 23

Ex 3.3 Class 11 Maths Question 24.
cos 4x = 1 – 8 sin2x cos2x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 24

Ex 3.3 Class 11 Maths Question 25.
cos 6x = 32 cos6 x – 48 cos4x + 18 cos2 x -1
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 25

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.3, drop a comment below and we will get back to you at the earliest.

Find the principal and general solutions of the following equations:
Ex 3.4 Class 11 Maths Question 1.
tanx=\sqrt { 3 }
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 1

Ex 3.4 Class 11 Maths Question 2.
sec x = 2
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 2

Ex 3.4 Class 11 Maths Question 3.
cotx=-\sqrt { 3 }
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 3
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 4

Ex 3.4 Class 11 Maths Question 4.
cosec x = -2
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 5

Find the general solution for each of the following equations:
Ex 3.4 Class 11 Maths Question 5.
cos 4x = cos 2x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 6

Ex 3.4 Class 11 Maths Question 6.
cos 3x + cos x – cos 2x=0
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 7

Ex 3.4 Class 11 Maths Question 7.
sin 2 x + cos x = 0
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 8

Ex 3.4 Class 11 Maths Question 8.
sec22x = 1 – tan 2x
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 9

Ex 3.4 Class 11 Maths Question 9.
sin x + sin 3x + sin 5x = 0
Solution.
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 10
NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 11

We hope the NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4 help you. If you have any query regarding NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.4, drop a comment below and we will get back to you at the earliest.

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