मराठी

CBSECommerce (English Medium) Class 11

प्रश्नपत्रिका

प्रश्नपत्रिका

पाठ्यपुस्तक उत्तरे१२७३४

MCQ ऑनलाइन सराव परीक्षा

महत्वाचे प्रश्न आणि उत्तरे

संकल्पना स्पष्टीकरण आणि व्हिडिओ३३८

टाइम टेबल

अभ्यासक्रम

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]

1.1Page 21

Find the general solution of the following equation:

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

1.2Page 21

Find the general solution of the following equation:

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

1.3Page 21

Find the general solution of the following equation:

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

1.4Page 21

Find the general solution of the following equation:

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

1.5Page 21

Find the general solution of the following equation:

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

1.6Page 21

Find the general solution of the following equation:

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

2.01Page 21

Find the general solution of the following equation:

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

2.02Page 21

Find the general solution of the following equation:

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

2.03Page 21

Find the general solution of the following equation:

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

2.04Page 21

Find the general solution of the following equation:

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

2.05Page 21

Find the general solution of the following equation:

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

2.06Page 21

Find the general solution of the following equation:

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

2.07Page 21

Find the general solution of the following equation:

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

2.08Page 21

Find the general solution of the following equation:

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

2.09Page 21

Find the general solution of the following equation:

\[\tan px = \cot qx\]

2.1Page 21

Find the general solution of the following equation:

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

2.11Page 21

Find the general solution of the following equation:

\[\sin x = \tan x\]

2.12Page 21

Find the general solution of the following equation:

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

3.1Page 22

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

3.2Page 22

Solve the following equation:

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

3.3Page 22

Solve the following equation:

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

3.4Page 22

Solve the following equation:

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

3.5Page 22

Solve the following equation:

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

3.6Page 22

Solve the following equation:

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

3.7Page 22

Solve the following equation:

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

4.1Page 22

Solve the following equation:

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

4.2Page 22

Solve the following equation:

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

4.3Page 22

Solve the following equation:

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

4.4Page 22

Solve the following equation:

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

4.5Page 22

Solve the following equation:

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

4.6Page 22

Solve the following equation:

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

4.7Page 22

Solve the following equation:

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

4.8Page 22

Solve the following equation:

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

4.9Page 22

Solve the following equation:

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

5.1Page 22

Solve the following equation:

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

5.2Page 22

Solve the following equation:

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

5.3Page 22

Solve the following equation:

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

6.1Page 22

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

6.2Page 22

Solve the following equation:

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

6.3Page 22

Solve the following equation:

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

6.4Page 22

Solve the following equation:

`cosec x = 1 + cot x`

7.1Page 22

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

7.2Page 22

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

7.3Page 22

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

7.4Page 22

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

7.5Page 22

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

7.6Page 22

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

7.7Page 22

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

7.8Page 22

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

7.9Page 22

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

8Page 22

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

9Page 22

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

10Page 22

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

13Page 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]

1Page 26

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

2Page 26

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

3Page 26

Write the general solutions of tan² 2x = 1.

4Page 26

Write the set of values of a for which the equation

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

5Page 26

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

6Page 26

Write the number of points of intersection of the curves

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

7Page 26

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

and cos 2x are in A.P.

8Page 26

Write the number of points of intersection of the curves

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

9Page 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].

10Page 26

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

11Page 26

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

12Page 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]

1Page 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`

2Page 26

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

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

3Page 27

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

AP
GP
HP
none of these

4Page 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

5Page 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

6Page 27

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

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

7Page 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

8Page 27

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

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

9Page 27

The smallest positive angle which satisfies the equation

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

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

10Page 27

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

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

11Page 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.

12Page 27

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

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

13Page 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

14Page 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

15Page 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

16Page 28

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

finite
infinite
one
no

17Page 28

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

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

18Page 28

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

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

19Page 28

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

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

20Page 28

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

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

21Page 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, Angles and Their Measurement in Higher Mathematics, Signs of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations, Trigonometric Ratios, Graphs of Trigonometric Functions, 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, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications.

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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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