Solutions of chapter 11. Trigonometric Equations | RD Sharma - Mathematics - Class 11

RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 11. Trigonometric Equations

Subject: Maths - Class 11^th

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Chapter Exercises

Exercise 11.1

Very Short Answer

MCQ

Exercise 11.1

1

Find the general solutions of the following equations :

i.

1

Find the general solutions of the following equations :

i.

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

1

Find the general solutions of the following equations :

2

Find the general solutions of the following equations :

2

Find the general solutions of the following equations :

2

Find the general solutions of the following equations :

2

Find the general solutions of the following equations :

2

Find the general solutions of the following equations :

sin 9x = sin x

2

Find the general solutions of the following equations :

sin 9x = sin x

2

Find the general solutions of the following equations :

sin 2x = cos 3x

2

Find the general solutions of the following equations :

sin 2x = cos 3x

2

Find the general solutions of the following equations :

tan x + cot 2x = 0

2

Find the general solutions of the following equations :

tan x + cot 2x = 0

2

Find the general solutions of the following equations :

tan 3x = cot x

2

Find the general solutions of the following equations :

tan 3x = cot x

2

Find the general solutions of the following equations :

tan 2x tan x = 1

2

Find the general solutions of the following equations :

tan 2x tan x = 1

2

Find the general solutions of the following equations :

tan mx + cot nx = 0

2

Find the general solutions of the following equations :

tan mx + cot nx = 0

2

Find the general solutions of the following equations :

tan px = cot qx

2

Find the general solutions of the following equations :

tan px = cot qx

2

Find the general solutions of the following equations :

sin 2x + cos x = 0

2

Find the general solutions of the following equations :

sin 2x + cos x = 0

2

Find the general solutions of the following equations :

sin x = tan x

2

Find the general solutions of the following equations :

sin x = tan x

2

Find the general solutions of the following equations :

sin 3x + cos 2x = 0

2

Find the general solutions of the following equations :

sin 3x + cos 2x = 0

3

Solve the following equations :

3

Solve the following equations :

3

Solve the following equations :

2 cos² x – 5 cos x + 2 =0

3

Solve the following equations :

2 cos² x – 5 cos x + 2 =0

3

Solve the following equations :

3

Solve the following equations :

3

Solve the following equations :

4 sin² x – 8 cos x + 1 = 0

3

Solve the following equations :

4 sin² x – 8 cos x + 1 = 0

3

Solve the following equations :

3

Solve the following equations :

3

Solve the following equations :

3

Solve the following equations :

3

Solve the following equations :

cos 4x = cos 2x

3

Solve the following equations :

cos 4x = cos 2x

4

Solve the following equations :

cos x + cos 2x + cos 3x = 0

4

Solve the following equations :

cos x + cos 2x + cos 3x = 0

4

Solve the following equations :

cos x + cos 3x – cos 2x = 0

4

Solve the following equations :

cos x + cos 3x – cos 2x = 0

4

Solve the following equations :

sin x + sin 5x = sin 3x

4

Solve the following equations :

sin x + sin 5x = sin 3x

4

Solve the following equations :

cos x cos 2x cos 3x = �

4

Solve the following equations :

cos x cos 2x cos 3x = �

4

Solve the following equations :

cos x + sin x = cos 2x + sin 2x

4

Solve the following equations :

cos x + sin x = cos 2x + sin 2x

4

Solve the following equations :

sin x + sin 2x + sin 3x = 0

4

Solve the following equations :

sin x + sin 2x + sin 3x = 0

4

Solve the following equations :

sin x + sin 2x + sin 3x + sin 4x = 0

4

Solve the following equations :

sin x + sin 2x + sin 3x + sin 4x = 0

4

Solve the following equations :

sin 3x – sin x = 4 cos² x – 2

4

Solve the following equations :

sin 3x – sin x = 4 cos² x – 2

4

Solve the following equations :

sin 2x – sin 4x + sin 6x = 0

4

Solve the following equations :

sin 2x – sin 4x + sin 6x = 0

5

Solve the following equations :

tan x + tan 2x + tan 3x = 0

5

Solve the following equations :

tan x + tan 2x + tan 3x = 0

5

Solve the following equations :

tan x + tan 2x = tan 3x

5

Solve the following equations :

tan x + tan 2x = tan 3x

5

Solve the following equations :

tan 3x + tan x = 2 tan 2x

5

Solve the following equations :

tan 3x + tan x = 2 tan 2x

6

Solve the following equations :

6

Solve the following equations :

6

Solve the following equations :

6

Solve the following equations :

6

Solve the following equations :

sin x + cos x = 1

6

Solve the following equations :

sin x + cos x = 1

6

Solve the following equations :

cosec x = 1 + cot x

6

Solve the following equations :

cosec x = 1 + cot x

6

Solve the following equations :

6

Solve the following equations :

7

Solve the following equations :

cot x + tan x = 2

7

Solve the following equations :

cot x + tan x = 2

7

Solve the following equations :

2 sin² x = 3 cos x, 0 ≤ x ≤ 2π

7

Solve the following equations :

2 sin² x = 3 cos x, 0 ≤ x ≤ 2π

7

Solve the following equations :

sec x cos 5x + 1 = 0, 0 < x < π/2

7

Solve the following equations :

sec x cos 5x + 1 = 0, 0 < x < π/2

7

Solve the following equations :

5 cos² x + 7 sin² x – 6 = 0

7

Solve the following equations :

5 cos² x + 7 sin² x – 6 = 0

7

Solve the following equations :

sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x

7

Solve the following equations :

sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x

7

Solve the following equations :

4 sin x cos x + 2 sin x + 2 cos x + 1 = 0

7

Solve the following equations :

4 sin x cos x + 2 sin x + 2 cos x + 1 = 0

7

Solve the following equations :

cos x + sin x = cos 2x + sin 2x

7

Solve the following equations :

cos x + sin x = cos 2x + sin 2x

7

Solve the following equations :

sin x tan x – 1 = tan x – sin x

7

Solve the following equations :

sin x tan x – 1 = tan x – sin x

7

Solve the following equations :

3 tan x + cot x = 5 cosec x

7

Solve the following equations :

3 tan x + cot x = 5 cosec x

8

Solve : 3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0

8

Solve : 3 – 2 cos x – 4 sin x – cos 2x + sin 2x = 0

9

3sin² x – 5 sin x cos x + 8 cos² x = 2

9

3sin² x – 5 sin x cos x + 8 cos² x = 2

10

Solve :

10

Solve :

Very Short Answer

1

Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].

2

Write the number of solutions of the equation 4 sin x – 3 cos x = 7.

3

Write the general solution of tan² 2x = 1.

4

Write the set of values of a for which the equation √3 sin x – cos x = a has no solution.

5

If cos x = k has exactly one solution in [0, 2 π], then write the value(s) of k.

6

Write the number of points of intersection of the curves 2y = 1 and y = cos x, 0 ≤ x ≤ 2π.

7

Write the values of x in [0, π] for which and cos 2x are in A.P.

8

Write the number of points of intersection of the curves 2y = - 1 and y = cosec x.

9

Write the solution set of the equation (2 cos x + 1) (4 cos x + 5) = 0 in the interval (0, 2 π].

10

Write the number of values of x in [0, 2 π] that satisfy the equation

11

If 3 tan (x - 15^o) = tan (x + 15^o), 0 ≤ x ≤ 90^o, find x.

12

If 2 sin² x = 3 cos x, where 0 ≤ x ≤ 2 π, then find the value of x.

13

If sec x cos 5x + 1 = 0, where find the value of x.

MCQ

1

Mark the Correct alternative in the following:

The smallest value of x satisfying the equation √3 (cot x + tan x) = 4 is

2

Mark the Correct alternative in the following:

If cos x + √3 sin x = 2, then x =

3

Mark the Correct alternative in the following:

If tan px – tan qx = 0, then the values of θ form a series in

4

Mark the Correct alternative in the following:

If a is any real number, the number of roots of cot x – tan x = a in the first quadrant is (are).

5

Mark the Correct alternative in the following:

The general solution of the equation 7 cos² x + 3 sin² x = 4 is

6

Mark the Correct alternative in the following:

A solution of the equation cos² x + sin x + 1 = 0, lies in the interval

7

Mark the Correct alternative in the following:

The number of solution in [0, π/2] of the equation cos 3x tan 5x = sin 7x is

8

Mark the Correct alternative in the following:

The general value of x satisfying the equation is given by

9

Mark the Correct alternative in the following:

The smallest positive angle which satisfies the equation is

10

Mark the Correct alternative in the following:

If 4 sin² x = 1, then the values of x are

11

Mark the Correct alternative in the following:

If cot x – tan x = sec x, then x is equal to

12

Mark the Correct alternative in the following:

A value of x satisfying is

13

Mark the Correct alternative in the following:

In (0, π), the number of solutions of the equation tan x + tan 2x + tan 3x = tan x tan 2x tan 3x is

14

Mark the Correct alternative in the following:

The number of values of x in [0, 2π] that satisfy the equation

15

Mark the Correct alternative in the following:

If e^{sin x} – e^{– sin x} – 4 = 0, then x =

16

Mark the Correct alternative in the following:

The equation 3 cos x + 4 sin x = 6 has …. Solution

17

Mark the Correct alternative in the following:

If then general value of θ is

18

Mark the Correct alternative in the following:

General solution of tan 5x = cot 2x is

19

Mark the Correct alternative in the following:

The solution of the equation cos² x + sin x + 1 = 0 lies in the interval

20

Mark the Correct alternative in the following:

If and 0 < x < 2 π, then the solution are

21

Mark the Correct alternative in the following:

The number of values of x in the interval [0. 5 π] satisfying the equation 3 sin² x – 7 sin x + 2 = 0 is