Solutions of chapter 15. Trigonometric, or Circular, Functions | RS Aggarwal - Mathematics - Class 11

RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 15. Trigonometric, or Circular, Functions

Subject: Maths - Class 11^th

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Chapter Exercises

Exercise 15A

Exercise 15B

Exercise 15C

Exercise 15D

Exercise 15E

Exercise 15A

1

If and θ lies in Quadrant III, find the value of all the other five trigonometric functions.

2

If and θ lies in Quadrant IV, find the values of all the other five trigonometric functions.

3

If and θ lies in Quadrant II, find the values of all the other five trigonometric functions.

4

If and θ lies in Quadrant IV, find the values of all the other five trigonometric functions.

5

If and x lies in Quadrant III, find the values of cos x and cot x.

6

If , find the value of sin x.

7

If , find the values of all the other five trigonometric functions.

8 A

Find the value of

8 B

Find the value of

8 C

Find the value of

8 D

Find the value of

8 E

Find the value of

8 F

Find the value of

9

Find the value of

sin 405°

9

Find the value of

sec (-1470⁰)

9

Find the value of

tan (-300⁰)

9

Find the value of

cot (585⁰)

9

Find the value of

cosec (-750⁰)

9

Find the value of

cos (-2220⁰)

10

Prove that

10 B

Prove that

10 C

Prove that

Exercise 15B

1

Find the value of

(i) cos 840⁰

(ii) sin 870⁰

(iii) tan ( - 120⁰)

(iv) sec ( - 420⁰)

(v) cosec ( - 690⁰)

(vi) tan (225⁰)

(vii) cot ( - 315⁰)

(viii) sin ( - 1230⁰)

(ix) cos (495⁰)

2

Find the values of all trigonometric functions of 135⁰

3

Prove that

(i)

(ii)

(iv)

(v)

4

Prove that

(i)

(ii)

5

Prove that

(i)

(ii)

6

Prove that

7

Prove that

(i)

(ii)

(iii) tan 15⁰ + cot 15⁰ = 4

8

Prove that

(i)

(ii)

(iii)

9

Prove that

10

Prove that

11

Prove that

12

Prove that

13

Prove that

14

If θ and Φ lie in the first quadrant such that , find the values of

(i) sin (θ - Φ )

(ii) cos (θ - Φ)

(iii) tan (θ - Φ)

15

If x and y are acute such that , prove that

16

If x and y are acute angles such that , prove that .

17

If, where

, find the values of

(i) sin (x + y)

(ii) cos (x + y)

(iii) tan (x – y)

18

If , where , find the values of

(i) sin (x + y)

(ii) cos (x – y)

(iii) tan (x + y)

19

Prove that

(i)

(ii)

(iii)

(iv)

20

Prove that

(i)

(ii)

(iii)

Exercise 15C

1

Prove that

sin(150⁰ + x) + sin (150⁰ – x) = cos x

2

Prove that

cos x + cos (120⁰ – x) + cos (120⁰ + x) = 0

3

Prove that

4

Prove that

5

Prove that

6

Express each of the following as a product.

1. sin 10x + sin 6x

2. sin 7x – sin 3x

3. cos 7x + cos 5x

4. cos2x – cos 4x

7

Express each of the following as an algebraic sum of sines or cosines :

(i) 2sin 6x cos 4x

(ii) 2cos 5x din 3x

(iii) 2cos 7x cos 3x

(iv) 2sin 8x sin 2x

8

Prove that

9

Prove that

10

Prove that

11

Prove that

12

Prove that

13

Prove that

14

Prove that

cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)

15

Prove that

(sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

16

Prove that

(cos x – cos y)² + (sin x – sin y)² = 4 sin²

17

Prove that

18

Prove that

19

Prove that

20

Prove that

21

Prove that

22

Prove that

23

Prove that

24

Prove that

25

Prove that

26

If , prove that

27 A

Prove that

27 B

Prove that

27

Prove that

Exercise 15D

1 A

If , find the values of

sin 2x

1

If , find the values of

cos 2x

1 C

If , find the values of

tan 2x

2 A

If , find the values of

sin 2x

2

If , find the values of

cos 2x

2

If , find the values of

tan 2x

3 A

If , find the values of

sin 2x

3

If , find the values of

cos 2x

3

If , find the values of

tan 2x

4

If , find the value of sin 3x.

4

If , find the value of cos 3x.

5

Prove that

6

Prove that

7

8

Prove that

9

Prove that

sin 2x(tan x + cot x) = 2

10

Prove that

cosec 2x + cot 2x = cot x

11

Prove that

cos 2x + 2sin²x = 1

12

Prove that

(sin x – cos x)² = 1 – sin 2x

13

Prove that

cot x – 2cot 2x = tan x

14

Prove that

15

Prove that

16

Prove that

17

Prove that

18 A

Prove that

18

Prove that

18 C

Prove that

18 D

Prove that

19 A

Prove that

19 B

Prove that

20

Prove that tan 6⁰ tan 42⁰ tan 66⁰ tan 78⁰ = 1

21

If , prove that

Exercise 15E

1

If , find the values of

(i) (ii)

(iii)

2

If , find the values of

(i) (ii)

(iii)

3

If lies in Quadrant IV, find the values of

(i) (ii)

(iii)

4

If lies in Quadrant I, find the values of

(i) sin x

(ii) cos x

(iii) cot x

5

If , find the value of .

6

Prove that

7

Prove that

8

Prove that

9

Prove that

10

Prove that