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

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RD Sharma Mathematics Class 11

Mathematics Class 11 - Shaalaa.com

Chapter 11: Trigonometric equations

Ex. 11.10Others

Chapter 11: Trigonometric equations Exercise 11.10 solutions [Pages 21 - 22]

Ex. 11.10 | Q 1.1 | Page 21

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]
Ex. 11.10 | Q 1.2 | Page 21

Find the general solution of the following equation:

\[\cos x = - \frac{\sqrt{3}}{2}\]
Ex. 11.10 | Q 1.3 | Page 21

Find the general solution of the following equation:

\[cosec x = - \sqrt{2}\]
Ex. 11.10 | Q 1.4 | Page 21

Find the general solution of the following equation:

\[\sec x = \sqrt{2}\]
Ex. 11.10 | Q 1.5 | Page 21

Find the general solution of the following equation:

\[\tan x = - \frac{1}{\sqrt{3}}\]
Ex. 11.10 | Q 1.6 | Page 21

Find the general solution of the following equation:

\[\sqrt{3} \sec x = 2\]
Ex. 11.10 | Q 2.01 | Page 21

Find the general solution of the following equation:

\[\sin 2x = \frac{\sqrt{3}}{2}\]
Ex. 11.10 | Q 2.02 | Page 21

Find the general solution of the following equation:

\[\cos 3x = \frac{1}{2}\]
Ex. 11.10 | Q 2.03 | Page 21

Find the general solution of the following equation:

\[\sin 9x = \sin x\]
Ex. 11.10 | Q 2.04 | Page 21

Find the general solution of the following equation:

\[\sin 2x = \cos 3x\]
Ex. 11.10 | Q 2.05 | Page 21

Find the general solution of the following equation:

\[\tan x + \cot 2x = 0\]
Ex. 11.10 | Q 2.06 | Page 21

Find the general solution of the following equation:

\[\tan 3x = \cot x\]
Ex. 11.10 | Q 2.07 | Page 21

Find the general solution of the following equation:

\[\tan 2x \tan x = 1\]
Ex. 11.10 | Q 2.08 | Page 21

Find the general solution of the following equation:

\[\tan mx + \cot nx = 0\]
Ex. 11.10 | Q 2.09 | Page 21

Find the general solution of the following equation:

\[\tan px = \cot qx\]

 

Ex. 11.10 | Q 2.1 | Page 21

Find the general solution of the following equation:

\[\sin 2x + \cos x = 0\]
Ex. 11.10 | Q 2.11 | Page 21

Find the general solution of the following equation:

\[\sin x = \tan x\]
Ex. 11.10 | Q 2.12 | Page 21

Find the general solution of the following equation:

\[\sin 3x + \cos 2x = 0\]
Ex. 11.10 | Q 3.1 | Page 22

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

Ex. 11.10 | Q 3.2 | Page 22

Solve the following equation:

\[2 \cos^2 x - 5 \cos x + 2 = 0\]
Ex. 11.10 | Q 3.3 | Page 22

Solve the following equation:

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\]
Ex. 11.10 | Q 3.4 | Page 22

Solve the following equation:

\[4 \sin^2 x - 8 \cos x + 1 = 0\]
Ex. 11.10 | Q 3.5 | Page 22

Solve the following equation:

\[\tan^2 x + \left( 1 - \sqrt{3} \right) \tan x - \sqrt{3} = 0\]
Ex. 11.10 | Q 3.6 | Page 22

Solve the following equation:

\[3 \cos^2 x - 2\sqrt{3} \sin x \cos x - 3 \sin^2 x = 0\]
Ex. 11.10 | Q 3.7 | Page 22

Solve the following equation:

\[\cos 4 x = \cos 2 x\]
Ex. 11.10 | Q 4.1 | Page 22

Solve the following equation:

\[\cos x + \cos 2x + \cos 3x = 0\]
Ex. 11.10 | Q 4.2 | Page 22

Solve the following equation:

\[\cos x + \cos 3x - \cos 2x = 0\]
Ex. 11.10 | Q 4.3 | Page 22

Solve the following equation:

\[\sin x + \sin 5x = \sin 3x\]
Ex. 11.10 | Q 4.4 | Page 22

Solve the following equation:

\[\cos x \cos 2x \cos 3x = \frac{1}{4}\]
Ex. 11.10 | Q 4.5 | Page 22

Solve the following equation:

\[\cos x + \sin x = \cos 2x + \sin 2x\]
Ex. 11.10 | Q 4.6 | Page 22

Solve the following equation:

\[\sin x + \sin 2x + \sin 3 = 0\]
Ex. 11.10 | Q 4.7 | Page 22

Solve the following equation:

\[\sin x + \sin 2x + \sin 3x + \sin 4x = 0\]
Ex. 11.10 | Q 4.8 | Page 22

Solve the following equation:

\[\sin 3x - \sin x = 4 \cos^2 x - 2\]
Ex. 11.10 | Q 4.9 | Page 22

Solve the following equation:

\[\sin 2x - \sin 4x + \sin 6x = 0\]
Ex. 11.10 | Q 5.1 | Page 22

Solve the following equation:

\[\tan x + \tan 2x + \tan 3x = 0\]
Ex. 11.10 | Q 5.2 | Page 22

Solve the following equation:

\[\tan x + \tan 2x = \tan 3x\]
Ex. 11.10 | Q 5.3 | Page 22

Solve the following equation:

\[\tan 3x + \tan x = 2\tan 2x\]
Ex. 11.10 | Q 6.1 | Page 22

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

Ex. 11.10 | Q 6.2 | Page 22

Solve the following equation:

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

Ex. 11.10 | Q 6.3 | Page 22

Solve the following equation:

\[\sin x + \cos x = 1\]
Ex. 11.10 | Q 6.4 | Page 22

Solve the following equation:

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

Ex. 11.10 | Q 7.1 | Page 22

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

 

Ex. 11.10 | Q 7.2 | Page 22

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

Ex. 11.10 | Q 7.3 | Page 22

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

Ex. 11.10 | Q 7.4 | Page 22

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

Ex. 11.10 | Q 7.5 | Page 22

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

Ex. 11.10 | Q 7.6 | Page 22

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

Ex. 11.10 | Q 7.7 | Page 22

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

 

Ex. 11.10 | Q 7.8 | Page 22

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

 

Ex. 11.10 | Q 7.9 | Page 22

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

Ex. 11.10 | Q 8 | Page 22

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

Ex. 11.10 | Q 9 | Page 22

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

Ex. 11.10 | Q 10 | Page 22

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

Ex. 11.10 | Q 13 | Page 22

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

Chapter 11: Trigonometric equations solutions [Page 26]

Q 1 | Page 26

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

Q 2 | Page 26

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

Q 3 | Page 26

Write the general solutions of tan2 2x = 1.

 
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.
Q 5 | Page 26

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

 
Q 6 | Page 26

Write the number of points of intersection of the curves

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

Q 8 | Page 26

Write the number of points of intersection of the curves

\[2y = - 1 \text{ and }y = cosec x\]
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].
Q 10 | Page 26

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

Q 11 | Page 26

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

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.

Chapter 11: Trigonometric equations solutions [Pages 26 - 28]

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`

Q 2 | Page 26

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

 

  • \[\pi/3\]

     

  • \[2\pi/3\]

     

  • \[4\pi/6\]

     

  • \[5\pi/12\]

     

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

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

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

Q 6 | Page 27

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

  • \[\left( - \pi/4, \pi/4 \right)\]

     

  • \[\left( \pi/4, 3\pi/4 \right)\]

     

  • \[\left( 3\pi/4, 5\pi/4 \right)\]

     

  • \[\left( 5\pi/4, 7\pi/4 \right)\]

     

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

Q 8 | Page 27

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

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

     

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

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

     

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

Q 9 | Page 27

The smallest positive angle which satisfies the equation ​

\[2 \sin^2 x + \sqrt{3} \cos x + 1 = 0\] is
  • \[\frac{5\pi}{6}\]

     

  • \[\frac{2\pi}{3}\]

     

  • \[\frac{\pi}{3}\]

     

  • \[\frac{\pi}{6}\]

     

Q 10 | Page 27

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

 

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

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

     

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

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

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`

  • \[\frac{\pi}{3}\]

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

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

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

Q 16 | Page 28

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

  • finite

  • infinite

  • one

  • no

Q 17 | Page 28

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

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

     

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

  • \[n \pi + \frac{\pi}{4} - \frac{\pi}{3}, n \in Z\]

     

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

Q 18 | Page 28

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

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

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

     

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

     

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

     

Q 19 | Page 28

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

  • \[\left( - \pi/4, \pi/4 \right)\]

     

  • \[\left(\pi/4,3 \pi/4 \right)\]

     

  • \[\left( 3\pi/4, 5\pi/4 \right)\]

     

  • \[\left( 5\pi/4, 7\pi/4 \right)\]

     

Q 20 | Page 28

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

  • \[x = \frac{\pi}{3}, \frac{4\pi}{3}\]

     

  • \[x = \frac{2\pi}{3}, \frac{4\pi}{3}\]

     

  • \[x = \frac{2\pi}{3}, \frac{7\pi}{6}\]

     

  • \[\theta = \frac{2\pi}{3}, \frac{5\pi}{3}\]

     

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

Chapter 11: Trigonometric equations

Ex. 11.10Others

RD Sharma Mathematics Class 11

Mathematics Class 11 - Shaalaa.com

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

RD Sharma solutions for Class 11 Maths 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 Mathematics Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing 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 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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