# 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). −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:**

**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.**