#### Chapters

Chapter 2: Relations

Chapter 3: Functions

Chapter 4: Measurement of Angles

Chapter 5: Trigonometric Functions

Chapter 6: Graphs of Trigonometric Functions

Chapter 7: Values of Trigonometric function at sum or difference of angles

Chapter 8: Transformation formulae

Chapter 9: Values of Trigonometric function at multiples and submultiples of an angle

Chapter 10: Sine and cosine formulae and their applications

Chapter 11: Trigonometric equations

Chapter 12: Mathematical Induction

Chapter 13: Complex Numbers

Chapter 14: Quadratic Equations

Chapter 15: Linear Inequations

Chapter 16: Permutations

Chapter 17: Combinations

Chapter 18: Binomial Theorem

Chapter 19: Arithmetic Progression

Chapter 20: Geometric Progression

Chapter 21: Some special series

Chapter 22: Brief review of cartesian system of rectangular co-ordinates

Chapter 23: The straight lines

Chapter 24: The circle

Chapter 25: Parabola

Chapter 26: Ellipse

Chapter 27: Hyperbola

Chapter 28: Introduction to three dimensional coordinate geometry

Chapter 29: Limits

Chapter 30: Derivatives

Chapter 31: Mathematical reasoning

Chapter 32: Statistics

Chapter 33: Probability

## Chapter 11: Trigonometric equations

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 11 Trigonometric equations Exercise 11.1 [Pages 21 - 22]

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

**Find the general solution of the following equation:**

Solve the following equation:

\[\sin^2 x - \cos x = \frac{1}{4}\]

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

Solve the following equation:

\[\sin x + \cos x = \sqrt{2}\]

Solve the following equation:

\[\sqrt{3} \cos x + \sin x = 1\]

Solve the following equation:

Solve the following equation:

\[cosec x = 1 + \cot x\]

Solve the following equation:

\[\cot x + \tan x = 2\]

Solve the following equation:

\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]

Solve the following equation:

\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]

Solve the following equation:

\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]

Solve the following equation:

\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]

Solve the following equation:

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

Solve the following equation:

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

Solve the following equation:

sin x tan x – 1 = tan x – sin x

Solve the following equation:

3tanx + cot x = 5 cosec x

Solve the following equation:

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

Solve the following equation:

3sin^{2}x – 5 sin x cos x + 8 cos^{2} x = 2

Solve the following equation:

\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]

If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 11 Trigonometric equations Exercise 11.2 [Page 26]

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

Write the number of solutions of the equation

\[4 \sin x - 3 \cos x = 7\]

Write the general solutions of tan^{2} 2x = 1.

Write the set of values of a for which the equation

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

Write the number of points of intersection of the curves

Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]

and cos 2x are in A.P.

Write the number of points of intersection of the curves

Write the solution set of the equation

Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].

If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.

If \[2 \sin^2 x = 3\cos x\]. where \[0 \leq x \leq 2\pi\], then find the value of x.

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 11 Trigonometric equations Exercise 11.3 [Pages 26 - 28]

The smallest value of x satisfying the equation

- \[2\pi/3\]
`pi/3`

`pi/6`

`pi/12`

If \[\cos x + \sqrt{3} \sin x = 2,\text{ then }x =\]

- \[\pi/3\]
- \[2\pi/3\]
- \[4\pi/6\]
- \[5\pi/12\]

If \[\tan px - \tan qx = 0\], then the values of θ form a series in

AP

GP

HP

none of these

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

2

0

1

none of these

The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is

- \[x = 2 n\pi \pm \frac{\pi}{6}, n \in Z\]
- \[x = 2 n\pi \pm \frac{2\pi}{3}, n \in Z\]
- \[x = n\pi \pm \frac{\pi}{3}, n \in Z\]
none of these

A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval

- \[\left( - \pi/4, \pi/4 \right)\]
- \[\left( \pi/4, 3\pi/4 \right)\]
- \[\left( 3\pi/4, 5\pi/4 \right)\]
- \[\left( 5\pi/4, 7\pi/4 \right)\]

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

5

7

6

none of these

The general value of x satisfying the equation

\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]

- \[x = n\pi + \left( - 1 \right)^n \frac{\pi}{4} + \frac{\pi}{3}, n \in Z\]
\[x = n\pi + \left( - 1 \right)^n \frac{\pi}{3} + \frac{\pi}{6}, n \in Z\]

- \[x = n\pi \pm \frac{\pi}{6}, n \in Z\]
\[x = n\pi \pm \frac{\pi}{3}, n \in Z\]

The smallest positive angle which satisfies the equation

- \[\frac{5\pi}{6}\]
- \[\frac{2\pi}{3}\]
- \[\frac{\pi}{3}\]
- \[\frac{\pi}{6}\]

If \[4 \sin^2 x = 1\], then the values of x are

\[2 n\pi \pm \frac{\pi}{3}, n \in Z\]

- \[n\pi \pm \frac{\pi}{3}, n \in Z\]
\[n\pi \pm \frac{\pi}{6}, n \in Z\]

- \[2 n\pi \pm \frac{\pi}{6}, n \in Z\]

If \[\cot x - \tan x = \sec x\], then, x is equal to

- \[2 n\pi + \frac{3\pi}{2}, n \in Z\]
\[n\pi + \left( - 1 \right)^n \frac{\pi}{6}, n \in Z\]

- \[n\pi + \frac{\pi}{2}, n \in Z\]
none of these.

A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is

`(5pi)/3`

\[\frac{4\pi}{3}\]

`(2pi)/3`

\[\frac{\pi}{3}\]

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

7

5

4

2

The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]

1

2

3

4

If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =

0

- \[\sin^{- 1} \left\{ \log_e \left( 2 - \sqrt{5} \right) \right\}\]
1

none of these

The equation \[3 \cos x + 4 \sin x = 6\] has .... solution.

finite

infinite

one

no

If \[\sqrt{3} \cos x + \sin x = \sqrt{2}\] , then general value of **x is

- \[n \pi + \left( - 1 \right)^n \frac{\pi}{4}, n \in Z\]
\[\left( - 1 \right)^n \frac{\pi}{4} - \frac{\pi}{3}, n \in Z\]

- \[n \pi + \frac{\pi}{4} - \frac{\pi}{3}, n \in Z\]
\[n \pi + \left( - 1 \right)^n \frac{\pi}{4} - \frac{\pi}{3}, n \in Z\]

General solution of \[\tan 5 x = \cot 2 x\] is

\[\frac{n \pi}{7} + \frac{\pi}{2}, n \in Z\]

- \[x = \frac{n \pi}{7} + \frac{\pi}{3}, n \in Z\]
- \[x = \frac{n \pi}{7} + \frac{\pi}{14}, n \in Z\]
- \[x = \frac{n \pi}{7} - \frac{\pi}{14}, n \in Z\]

The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval

- \[\left( - \pi/4, \pi/4 \right)\]
- \[\left(\pi/4,3 \pi/4 \right)\]
- \[\left( 3\pi/4, 5\pi/4 \right)\]
- \[\left( 5\pi/4, 7\pi/4 \right)\]

If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are

- \[x = \frac{\pi}{3}, \frac{4\pi}{3}\]
- \[x = \frac{2\pi}{3}, \frac{4\pi}{3}\]
- \[x = \frac{2\pi}{3}, \frac{7\pi}{6}\]
- \[\theta = \frac{2\pi}{3}, \frac{5\pi}{3}\]

The number of values of x in the interval [0, 5 π] satisfying the equation \[3 \sin^2 x - 7 \sin x + 2 = 0\] is

0

5

6

10

## Chapter 11: Trigonometric equations

## RD Sharma solutions for Class 11 Mathematics Textbook chapter 11 - Trigonometric equations

RD Sharma solutions for Class 11 Mathematics Textbook chapter 11 (Trigonometric equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics Textbook chapter 11 Trigonometric equations are Transformation Formulae, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications, 180 Degree Plusminus X Function, 2X Function, 3X Function, Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications, Concept of Angle, Introduction of Trigonometric Functions, Signs of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations, Truth of the Identity, Negative Function Or Trigonometric Functions of Negative Angles, 90 Degree Plusminus X Function, Conversion from One Measure to Another, Graphs of Trigonometric Functions.

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