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RD Sharma solutions for Mathematics [English] Class 11 chapter 11 - Trigonometric equations [Latest edition]

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Chapters

    1: Sets

    2: Relations

    3: Functions

    4: Measurement of Angles

    5: Trigonometric Functions

    6: Graphs of Trigonometric Functions

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

    8: Transformation formulae

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

    10: Sine and cosine formulae and their applications

▶ 11: Trigonometric equations

    12: Mathematical Induction

    13: Complex Numbers

    14: Quadratic Equations

    15: Linear Inequations

    16: Permutations

    17: Combinations

    18: Binomial Theorem

    19: Arithmetic Progression

    20: Geometric Progression

    21: Some special series

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

    23: The straight lines

    24: The circle

    25: Parabola

    26: Ellipse

    27: Hyperbola

    28: Introduction to three dimensional coordinate geometry

    29: Limits

    30: Derivatives

    31: Mathematical reasoning

    32: Statistics

    33: Probability

RD Sharma solutions for Mathematics [English] Class 11 chapter 11 - Trigonometric equations - Shaalaa.com

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Solutions for Chapter 11: Trigonometric equations

Below listed, you can find solutions for Chapter 11 of CBSE, Karnataka Board PUC RD Sharma for Mathematics [English] Class 11.

Exercise 11.1Exercise 11.2Exercise 11.3

Exercise 11.1 [Pages 21 - 22]

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

Exercise 11.1 | Q 1.1 | Page 21

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]

Exercise 11.1 | Q 1.2 | Page 21

Find the general solution of the following equation:

\[\cos x = - \frac{\sqrt{3}}{2}\]

Exercise 11.1 | Q 1.3 | Page 21

Find the general solution of the following equation:

\[cosec x = - \sqrt{2}\]

Exercise 11.1 | Q 1.4 | Page 21

Find the general solution of the following equation:

\[\sec x = \sqrt{2}\]

Exercise 11.1 | Q 1.5 | Page 21

Find the general solution of the following equation:

\[\tan x = - \frac{1}{\sqrt{3}}\]

Exercise 11.1 | Q 1.6 | Page 21

Find the general solution of the following equation:

\[\sqrt{3} \sec x = 2\]

Exercise 11.1 | Q 2.01 | Page 21

Find the general solution of the following equation:

\[\sin 2x = \frac{\sqrt{3}}{2}\]

Exercise 11.1 | Q 2.02 | Page 21

Find the general solution of the following equation:

\[\cos 3x = \frac{1}{2}\]

Exercise 11.1 | Q 2.03 | Page 21

Find the general solution of the following equation:

\[\sin 9x = \sin x\]

Exercise 11.1 | Q 2.04 | Page 21

Find the general solution of the following equation:

\[\sin 2x = \cos 3x\]

Exercise 11.1 | Q 2.05 | Page 21

Find the general solution of the following equation:

\[\tan x + \cot 2x = 0\]

Exercise 11.1 | Q 2.06 | Page 21

Find the general solution of the following equation:

\[\tan 3x = \cot x\]

Exercise 11.1 | Q 2.07 | Page 21

Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]

Exercise 11.1 | Q 2.08 | Page 21

Find the general solution of the following equation:

\[\tan mx + \cot nx = 0\]

Exercise 11.1 | Q 2.09 | Page 21

Find the general solution of the following equation:

\[\tan px = \cot qx\]

Exercise 11.1 | Q 2.1 | Page 21

Find the general solution of the following equation:

\[\sin 2x + \cos x = 0\]

Exercise 11.1 | Q 2.11 | Page 21

Find the general solution of the following equation:

\[\sin x = \tan x\]

Exercise 11.1 | Q 2.12 | Page 21

Find the general solution of the following equation:

\[\sin 3x + \cos 2x = 0\]

Exercise 11.1 | Q 3.1 | Page 22

Solve the following equation:
\[\sin^2 x - \cos x = \frac{1}{4}\]

Exercise 11.1 | Q 3.2 | Page 22

Solve the following equation:

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

Exercise 11.1 | Q 3.3 | Page 22

Solve the following equation:

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\]

Exercise 11.1 | Q 3.4 | Page 22

Solve the following equation:

\[4 \sin^2 x - 8 \cos x + 1 = 0\]

Exercise 11.1 | Q 3.5 | Page 22

Solve the following equation:

\[\tan^2 x + \left( 1 - \sqrt{3} \right) \tan x - \sqrt{3} = 0\]

Exercise 11.1 | Q 3.6 | Page 22

Solve the following equation:

\[3 \cos^2 x - 2\sqrt{3} \sin x \cos x - 3 \sin^2 x = 0\]

Exercise 11.1 | Q 3.7 | Page 22

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Exercise 11.1 | Q 4.1 | Page 22

Solve the following equation:

\[\cos x + \cos 2x + \cos 3x = 0\]

Exercise 11.1 | Q 4.2 | Page 22

Solve the following equation:

\[\cos x + \cos 3x - \cos 2x = 0\]

Exercise 11.1 | Q 4.3 | Page 22

Solve the following equation:

\[\sin x + \sin 5x = \sin 3x\]

Exercise 11.1 | Q 4.4 | Page 22

Solve the following equation:

\[\cos x \cos 2x \cos 3x = \frac{1}{4}\]

Exercise 11.1 | Q 4.5 | Page 22

Solve the following equation:

\[\cos x + \sin x = \cos 2x + \sin 2x\]

Exercise 11.1 | Q 4.6 | Page 22

Solve the following equation:

\[\sin x + \sin 2x + \sin 3 = 0\]

Exercise 11.1 | Q 4.7 | Page 22

Solve the following equation:

\[\sin x + \sin 2x + \sin 3x + \sin 4x = 0\]

Exercise 11.1 | Q 4.8 | Page 22

Solve the following equation:

\[\sin 3x - \sin x = 4 \cos^2 x - 2\]

Exercise 11.1 | Q 4.9 | Page 22

Solve the following equation:

\[\sin 2x - \sin 4x + \sin 6x = 0\]

Exercise 11.1 | Q 5.1 | Page 22

Solve the following equation:

\[\tan x + \tan 2x + \tan 3x = 0\]

Exercise 11.1 | Q 5.2 | Page 22

Solve the following equation:

\[\tan x + \tan 2x = \tan 3x\]

Exercise 11.1 | Q 5.3 | Page 22

Solve the following equation:

\[\tan 3x + \tan x = 2\tan 2x\]

Exercise 11.1 | Q 6.1 | Page 22

Solve the following equation:
\[\sin x + \cos x = \sqrt{2}\]

Exercise 11.1 | Q 6.2 | Page 22

Solve the following equation:

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

Exercise 11.1 | Q 6.3 | Page 22

Solve the following equation:

\[\sin x + \cos x = 1\]

Exercise 11.1 | Q 6.4 | Page 22

Solve the following equation:

`cosec x = 1 + cot x`

Exercise 11.1 | Q 7.1 | Page 22

Solve the following equation:
\[\cot x + \tan x = 2\]

Exercise 11.1 | Q 7.2 | Page 22

Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]

Exercise 11.1 | Q 7.3 | Page 22

Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]

Exercise 11.1 | Q 7.4 | Page 22

Solve the following equation:
\[5 \cos^2 x + 7 \sin^2 x - 6 = 0\]

Exercise 11.1 | Q 7.5 | Page 22

Solve the following equation:
\[\sin x - 3\sin2x + \sin3x = \cos x - 3\cos2x + \cos3x\]

Exercise 11.1 | Q 7.6 | Page 22

Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0

Exercise 11.1 | Q 7.7 | Page 22

Solve the following equation:
cosx + sin x = cos 2x + sin 2x

Exercise 11.1 | Q 7.8 | Page 22

Solve the following equation:
sin x tan x – 1 = tan x – sin x

Exercise 11.1 | Q 7.9 | Page 22

Solve the following equation:
3tanx + cot x = 5 cosec x

Exercise 11.1 | Q 8 | Page 22

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

Exercise 11.1 | Q 9 | Page 22

Solve the following equation:
3sin²x – 5 sin x cos x + 8 cos² x = 2

Exercise 11.1 | Q 10 | Page 22

Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]

Exercise 11.1 | Q 13 | Page 22

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

Exercise 11.2 [Page 26]

RD Sharma solutions for Mathematics [English] Class 11 11 Trigonometric equations Exercise 11.2 [Page 26]

Exercise 11.2 | Q 1 | Page 26

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

Exercise 11.2 | Q 2 | Page 26

Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]

Exercise 11.2 | Q 3 | Page 26

Write the general solutions of tan² 2x = 1.

Exercise 11.2 | Q 4 | Page 26

Write the set of values of a for which the equation

\[\sqrt{3} \sin x - \cos x = a\] has no solution.

Exercise 11.2 | Q 5 | Page 26

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

Exercise 11.2 | Q 6 | Page 26

Write the number of points of intersection of the curves

\[2y = 1\] and \[y = \cos x, 0 \leq x \leq 2\pi\].

Exercise 11.2 | Q 7 | Page 26

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

and cos 2x are in A.P.

Exercise 11.2 | Q 8 | Page 26

Write the number of points of intersection of the curves

\[2y = - 1 \text{ and }y = cosec x\]

Exercise 11.2 | Q 9 | Page 26

Write the solution set of the equation

\[\left( 2 \cos x + 1 \right) \left( 4 \cos x + 5 \right) = 0\] in the interval [0, 2π].

Exercise 11.2 | Q 10 | Page 26

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

Exercise 11.2 | Q 11 | Page 26

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

Exercise 11.2 | Q 12 | Page 26

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

Exercise 11.3 [Pages 26 - 28]

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

Exercise 11.3 | Q 1 | Page 26

The smallest value of x satisfying the equation

\[\sqrt{3} \left( \cot x + \tan x \right) = 4\] is

\[2\pi/3\]
`pi/3`
`pi/6`
`pi/12`

Exercise 11.3 | Q 2 | Page 26

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

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

Exercise 11.3 | Q 3 | Page 27

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

AP
GP
HP
none of these

Exercise 11.3 | Q 4 | Page 27

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

Exercise 11.3 | Q 5 | Page 27

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

Exercise 11.3 | Q 6 | Page 27

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

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

Exercise 11.3 | Q 7 | Page 27

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

5
7
6
none of these

Exercise 11.3 | Q 8 | Page 27

The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]

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

Exercise 11.3 | Q 9 | Page 27

The smallest positive angle which satisfies the equation

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\] is

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

Exercise 11.3 | Q 10 | Page 27

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

\[2 n\pi \pm \frac{\pi}{3}, n \in Z\]
\[n\pi \pm \frac{\pi}{3}, n \in Z\]
\[n\pi \pm \frac{\pi}{6}, n \in Z\]
\[2 n\pi \pm \frac{\pi}{6}, n \in Z\]

Exercise 11.3 | Q 11 | Page 27

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.

Exercise 11.3 | Q 12 | Page 27

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

`(5pi)/3`
\[\frac{4\pi}{3}\]
`(2pi)/3`
\[\frac{\pi}{3}\]

Exercise 11.3 | Q 13 | Page 27

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

Exercise 11.3 | Q 14 | Page 27

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

Exercise 11.3 | Q 15 | Page 27

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

Exercise 11.3 | Q 16 | Page 28

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

finite
infinite
one
no

Exercise 11.3 | Q 17 | Page 28

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

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

Exercise 11.3 | Q 18 | Page 28

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

\[\frac{n \pi}{7} + \frac{\pi}{2}, n \in Z\]
\[x = \frac{n \pi}{7} + \frac{\pi}{3}, n \in Z\]
\[x = \frac{n \pi}{7} + \frac{\pi}{14}, n \in Z\]
\[x = \frac{n \pi}{7} - \frac{\pi}{14}, n \in Z\]

Exercise 11.3 | Q 19 | Page 28

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

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

Exercise 11.3 | Q 20 | Page 28

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

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

Exercise 11.3 | Q 21 | Page 28

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

Solutions for 11: Trigonometric equations

Exercise 11.1Exercise 11.2Exercise 11.3

RD Sharma solutions for Mathematics [English] Class 11 chapter 11 - Trigonometric equations - Shaalaa.com

RD Sharma solutions for Mathematics [English] Class 11 chapter 11 - Trigonometric equations

Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RD Sharma solutions for Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC 11 (Trigonometric equations) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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

Concepts covered in Mathematics [English] Class 11 chapter 11 Trigonometric equations are Transformation Formulae, 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, Trigonometric Functions, 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, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications.

Using RD Sharma Mathematics [English] Class 11 solutions Trigonometric equations exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in RD Sharma Solutions are essential questions that can be asked in the final exam. Maximum CBSE, Karnataka Board PUC Mathematics [English] Class 11 students prefer RD Sharma Textbook Solutions to score more in exams.

Get the free view of Chapter 11, Trigonometric equations Mathematics [English] Class 11 additional questions for Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC, and you can use Shaalaa.com to keep it handy for your exam preparation.

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