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 5: Trigonometric Functions
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 5 Trigonometric Functions Exercise 5.1 [Pages 18 - 19]
Prove the following identites
sec4x - sec2x = tan4x + tan2x
Prove the following identities
\[\sin^6 x + \cos^6 x = 1 - 3 \sin^2 x \cos^2 x\]
Prove the following identities
\[\left( cosec x - \sin x \right) \left( \sec x - \cos x \right) \left( \tan x + \cot x \right) = 1\]
Prove the following identities
\[cosec x \left( \sec x - 1 \right) - \cot x \left( 1 - \cos x \right) = \tan x - \sin x\]
Prove the following identities
\[\frac{1 - \sin x \cos x}{\cos x \left( \sec x - cosec x \right)} \cdot \frac{\sin^2 x - \cos^2 x}{\sin^3 x + \cos^3 x} = \sin x\]
Prove the following identitie
Prove the following identities
\[\frac{\sin^3 x + \cos^3 x}{\sin x + \cos x} + \frac{\sin^3 x - \cos^3 x}{\sin x - \cos x} = 2\]
Prove the following identities
\[\left( \sec x \sec y + \tan x \tan y \right)^2 - \left( \sec x \tan y + \tan x \sec y \right)^2 = 1\]
Prove the following identities
\[\frac{\cos x}{1 - \sin x} = \frac{1 + \cos x + \sin x}{1 + \cos x - \sin x}\]
Prove the following identities
Prove the following identities
\[1 - \frac{\sin^2 x}{1 + \cot x} - \frac{\cos^2 x}{1 + \tan x} = \sin x \cos x\]
Prove the following identities
Prove the following identities
\[\left( 1 + \tan \alpha \tan \beta \right)^2 + \left( \tan \alpha - \tan \beta \right)^2 = \sec^2 \alpha \sec^2 \beta\]
Prove the following identities
Prove the following identities
Prove the following identities
If \[x = \frac{2 \sin x}{1 + \cos x + \sin x}\], then prove that
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[\tan x = \frac{a}{b},\] show that
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
If \[\cot x \left( 1 + \sin x \right) = 4 m \text{ and }\cot x \left( 1 - \sin x \right) = 4 n,\] \[\left( m^2 + n^2 \right)^2 = mn\]
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
Prove the:
\[ \sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}} = - \frac{2}{\cos x},\text{ where }\frac{\pi}{2} < x < \pi\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[2 T_6 - 3 T_4 + 1 = 0\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 5 Trigonometric Functions Exercise 5.2 [Page 25]
Find the value of the other five trigonometric functions
Find the value of the other five trigonometric functions
Find the value of the other five trigonometric functions
\[\tan x = \frac{3}{4},\] x in quadrant III
Find the value of the other five trigonometric functions
\[\sin x = \frac{3}{5},\] x in quadrant I
If sin \[x = \frac{12}{13}\] and x lies in the second quadrant, find the value of sec x + tan x.
If sin\[x = \frac{3}{5}, \tan y = \frac{1}{2}\text{ and }\frac{\pi}{2} < x < \pi < y < \frac{3\pi}{2},\] find the value of 8 tan \[x - \sqrt{5} \sec y\]
If sin x + cos x = 0 and x lies in the fourth quadrant, find sin x and cos x.
If \[\cos x = - \frac{3}{5}\text{ and }\pi < x < \frac{3\pi}{2}\] find the values of other five trigonometric functions and hence evaluate \[\frac{cosec x + \cot x}{\sec x - \tan x}\]
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 5 Trigonometric Functions Exercise 5.3 [Pages 39 - 40]
Find the value of the following trigonometric ratio:
Find the value of the following trigonometric ratio:
sin 17π
Find the value of the following trigonometric ratio:
\[\tan\frac{11\pi}{6}\]
Find the value of the following trigonometric ratio:
Find the value of the following trigonometric ratio:
\[\tan \frac{7\pi}{4}\]
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Find the values of the following trigonometric ratio:
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that:
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
Prove that: tan (−225°) cot (−405°) −tan (−765°) cot (675°) = 0
Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
Prove that:
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that
Prove that
Prove that
Prove that
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
In a ∆ABC, prove that:
In a ∆ABC, prove that:
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
Prove that:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
Prove that:
Prove that:
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 5 Trigonometric Functions [Pages 40 - 41]
Write the maximum and minimum values of cos (cos x).
Write the maximum and minimum values of sin (sin x).
Write the maximum value of sin (cos x).
If sin x = cos2 x, then write the value of cos2 x (1 + cos2 x).
If sin x + cosec x = 2, then write the value of sinn x + cosecn x.
If sin x + sin2 x = 1, then write the value of cos12 x + 3 cos10 x + 3 cos8 x + cos6 x.
If sin x + sin2 x = 1, then write the value of cos8 x + 2 cos6 x + cos4 x.
If sin θ1 + sin θ2 + sin θ3 = 3, then write the value of cos θ1 + cos θ2 + cos θ3.
Write the value of sin 10° + sin 20° + sin 30° + ... + sin 360°.
A circular wire of radius 15 cm is cut and bent so as to lie along the circumference of a loop of radius 120 cm. Write the measure of the angle subtended by it at the centre of the loop.
Write the value of 2 (sin6 x + cos6 x) −3 (sin4 x + cos4 x) + 1.
Write the value of cos 1° + cos 2° + cos 3° + ... + cos 180°.
If cot (α + β) = 0, then write the value of sin (α + 2β).
If tan A + cot A = 4, then write the value of tan4 A + cot4 A.
Write the least value of cos2 x + sec2 x.
If 3 sin x + 5 cos x = 5, then write the value of 5 sin x − 3 cos x.
RD Sharma solutions for Class 11 Mathematics Textbook Chapter 5 Trigonometric Functions [Pages 41 - 43]
If tan x = \[x - \frac{1}{4x}\], then sec x − tan x is equal to
\[- 2x, \frac{1}{2x}\]
\[- \frac{1}{2x}, 2x\]
2x
\[2x, \frac{1}{2x}\]
If sec \[x = x + \frac{1}{4x}\], then sec x + tan x =
- \[x, \frac{1}{x}\]
- \[2x, \frac{1}{2x}\]
- \[- 2x, \frac{1}{2x}\]
- \[- \frac{1}{x}, x\]
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
sec x − tan x
sec x + tan x
tan x − sec x
none of these
cosec x + cot x
cosec x − cot x
−cosec x + cot x
−cosec x − cot x
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
- \[\cot\frac{x}{2}\]
- \[\tan\frac{x}{2}\]
- \[\cot\frac{x}{2} + \tan\frac{x}{2}\]
- \[\cot\frac{x}{2} - \tan\frac{x}{2}\]
If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to
2 sec x
−2 sec x
sec x
−sec x
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
θ, ϕ
r, θ
r, ϕ
r
If tan x + sec x = \[\sqrt{3}\], 0 < x < π, then x is equal to
- \[\frac{5\pi}{6}\]
- \[\frac{2\pi}{3}\]
- \[\frac{\pi}{6}\]
- \[\frac{\pi}{3}\]
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
- \[\frac{\sqrt{5}}{\sqrt{6}}\]
- \[\frac{2}{\sqrt{6}}\]
- \[\frac{1}{2}\]
- \[\frac{1}{\sqrt{6}}\]
If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
1 − cot α
1 + cot α
−1 + cot α
−1 −cot α
sin6 A + cos6 A + 3 sin2 A cos2 A =
0
1
2
3
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
- \[\frac{5}{3}\]
- \[\frac{3}{5}\]
- \[- \frac{3}{5}\]
- \[- \frac{5}{3}\]
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
- \[\frac{21}{22}\]
- \[\frac{15}{16}\]
- \[\frac{44}{117}\]
- \[\frac{117}{44}\]
x + y ≠ 0
x = y, x ≠ 0
x = y
x ≠0, y ≠ 0
If x is an acute angle and \[\tan x = \frac{1}{\sqrt{7}}\], then the value of \[\frac{{cosec}^2 x - \sec^2 x}{{cosec}^2 x + \sec^2 x}\] is
3/4
1/2
2
5/4
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
7
8
9.5
10
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
1
4
2
0
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
110
191
80
194
If x sin 45° cos2 60° = \[\frac{\tan^2 60^\circ cosec30^\circ}{\sec45^\circ \cot^{2^\circ} 30^\circ}\], then x =
2
4
8
16
If A lies in second quadrant 3tan A + 4 = 0, then the value of 2cot A − 5cosA + sin A is equal to
- \[- \frac{53}{10}\]
- \[\frac{23}{10}\]
- \[\frac{37}{10}\]
- \[\frac{7}{10}\]
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
- \[\frac{21}{22}\]
- \[\frac{15}{16}\]
- \[\frac{44}{117}\]
- \[\frac{117}{43}\]
If tan θ + sec θ =ex, then cos θ equals
- \[\frac{e^x + e^{- x}}{2}\]
- \[\frac{2}{e^x + e^{- x}}\]
- \[\frac{e^x - e^{- x}}{2}\]
- \[\frac{e^x - e^{- x}}{e^x + e^{- x}}\]
If sec x + tan x = k, cos x =
- \[\frac{k^2 + 1}{2k}\]
- \[\frac{2k}{k^2 + 1}\]
- \[\frac{k}{k^2 + 1}\]
- \[\frac{k}{k^2 - 1}\]
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
f(x) < 1
f(x) = 1
1 < f(x) < 2
f(x) ≥ 2
Which of the following is incorrect?
- \[\sin x = - \frac{1}{5}\]
cos x = 1
- \[\sec x = \frac{1}{2}\]
tan x = 20
The value of \[\cos1^\circ \cos2^\circ \cos3^\circ . . . \cos179^\circ\] is
- \[\frac{1}{\sqrt{2}}\]
0
1
-1
The value of \[\tan1^\circ \tan2^\circ \tan3^\circ . . . \tan89^\circ\] is
0
1
- \[\frac{1}{2}\]
not defined
Which of the following is correct?
- \[\sin1^\circ > \sin1\]
- \[\sin1^\circ < \sin1\]
- \[\sin1^\circ = \sin1\]
- \[\sin1^\circ = \frac{\pi}{180}\sin1\]
Chapter 5: Trigonometric Functions

RD Sharma solutions for Class 11 Mathematics Textbook chapter 5 - Trigonometric Functions
RD Sharma solutions for Class 11 Mathematics Textbook chapter 5 (Trigonometric Functions) 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 5 Trigonometric Functions 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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