Get Free **NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1, Ex 3.2, Ex 3.3, Ex 3.4, and Miscellaneous Exercise** PDF in Hindi and English Medium. Trigonometric Functions Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Trigonometric Functions All Exercises Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers.

- Trigonometric Functions Class 11 Ex 3.1
- Trigonometric Functions Class 11 Ex 3.2
- Trigonometric Functions Class 11 Ex 3.3
- Trigonometric Functions Class 11 Ex 3.4
- Trigonometric Functions Class 11 Miscellaneous Exercise

Free download NCERT Solutions for Class 11 Maths Chapter 3** Trigonometric Functions Ex 3.1, Ex 3.2, Ex 3.3, Ex 3.4, and Miscellaneous Exercise** PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

## 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 Maths Question 1:**

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**Ex 3.1 Class 11 Maths Question 2:**

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**More Resources for CBSE Class 11**

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- NCERT Solutions Class 11 Chemistry
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- NCERT Solutions Class 11 Business Studies
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- NCERT Solutions Class 11 Psychology
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- NCERT Solutions Class 11 Indian Economic Development
- NCERT Solutions Class 11 Computer Science

**Ex 3.1 Class 11 Maths Question 3:**

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**Ex 3.1 Class 11 Maths Question 7:**

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**NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2**

**Ex 3.2 Class 11 Maths Question 1:**

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**Ex 3.2 Class 11 Maths Question 3:**

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**Ex 3.2 Class 11 Maths Question 8:**

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**Ex 3.2 Class 11 Maths Question 9:**

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**Ex 3.2 Class 11 Maths Question 10:**

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**NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.3**

**Ex 3.3 Class 11 Maths Question 1:**

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**Ex 3.3 Class 11 Maths Question 3:**

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**Ex 3.3 Class 11 Maths Question 5:**

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**Ex 3.3 Class 11 Maths Question 6:**

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**Ex 3.3 Class 11 Maths Question 7:**

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**Ex 3.3 Class 11 Maths Question 8:**

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**Ex 3.3 Class 11 Maths Question 9:**

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**Ex 3.3 Class 11 Maths Question 10:**

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**Ex 3.3 Class 11 Maths Question 11:**

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**Ex 3.3 Class 11 Maths Question 13:**

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**Ex 3.3 Class 11 Maths Question 24:**

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**Ex 3.3 Class 11 Maths Question 25:**

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**Class 11 Maths NCERT Solutions Chapter 3 ****Exercise 3.4**

**Ex 3.4 Class 11 Maths Question 1:**

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**Ex 3.4 Class 11 Maths Question 3:**

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**Ex 3.4 Class 11 Maths Question 7:**

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**Ex 3.4 Class 11 Maths Question 8:**

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**Ex 3.4 Class 11 Maths Question 9:**

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**NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise**

**Miscellaneous Exercise Class 11 Maths Question 1:**

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**Miscellaneous Exercise Class 11 Maths Question 2:**

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**Miscellaneous Exercise Class 11 Maths Question 3:**

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**Miscellaneous Exercise Class 11 Maths Question 4:**

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**Miscellaneous Exercise Class 11 Maths Question 6:**

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**Miscellaneous Exercise Class 11 Maths Question 7:**

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**Miscellaneous Exercise Class 11 Maths Question 9:**

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**Miscellaneous Exercise Class 11 Maths 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 = ]**

**(i) **

**(ii) -4**

**(iii) **

**(iv) **

**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 = 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 = , where y lies in second quadrant.**

** Q.3: ****Find the values of other five trigonometric functions if coty=, where y lies in the third quadrant.**

**Q.4: Find the values of other five trigonometric if ****secy=, where y lies in the fourth quadrant.**

**Q.5: Find the values of other five trigonometric function if tan y = 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 .**

**Q.9: Calculate the value of the trigonometric function ****sin .**

**Q.10: Calculate the value of the trigonometric function** **cot **

**Exercise 3.3**

**Q.1: Prove:**

**sin²+cos²–tan²= **

**Q.2: Prove:**

**2sin²+cosec²6cos²=**

**Q.3: Prove:**

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

**Q.4: Prove:**

**2sin²+2cos²+2sec²=10**

**Q.5: Calculate the value of:**

**(i). sin75∘**

**(ii). tan15∘**

**Q.6:Prove:**

**cos(–x)cos(–y)–sin(–x)sin(–y)=sin(x+y)**

**Q.7: Prove:**

**Q.8: Prove:**

**Q.9: Prove:**

**Q.10: Prove:**

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

**Q.11 Prove:**

**=−√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:**

**Q.17: Prove:**

**Q.18: Prove:**

**Q.19: Prove:**

**Q.20: Prove:**

**Q.21: Prove:**

**Q.22: Prove:**

**cotxcot2x–cot2xcot3x–cot3xcotx=1**

**Q.23: Prove:**

**Q.24: Prove:**

**cos4x=1–8sin²xcos²x**

**Q.25: Prove:**

**cos6x=32cos ^{6}x–48cos^{4}x+18cos^{2}x−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:**

**Q.2: Prove that:**

**(sin3x+sinx)sinx+(cos3x–cosx)cosx=0**

**Q-3: Prove that:**

**(cosx+cosy)²+(sinx–siny)²=4cos²**

**Q-4: Prove that:**

**(cosx–cosy)²+(sinx–siny)²=4sin²**

**Q-5: Prove that:**

**sinx+sin3x+sin5x+sin7x=4cosxcos2xcos4x**

**Q-6: Prove that:**

**Q-7: Show that: sin3y+sin2y–siny=4sinycoscos**

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

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

**.**

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

### NCERT Solutions for Class 11 Maths All Chapters

- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutation and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability