NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Miscellaneous Exercise

The miscellaneous exercise contains questions covering the entire topics present in the chapter.

The Miscellaneous Exercise of NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions is based on the following topics:

  1. Angles
  2. Trigonometric Functions
  3. Trigonometric Functions of Sum and Difference of Two Angles
  4. Trigonometric Equations

These solutions provided here are based on the guidelines prescribed by the CBSE. The NCERT Solutions for class 11 can help the students in preparing well for the exams of class 11 exams.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Miscellaneous Exercise

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Access other exercise solutions of Class 11 Maths Chapter 3- Trigonometric Functions

Exercise 3.1 Solutions 7 Questions

Exercise 3.2 Solutions 10 Questions

Exercise 3.3 Solutions 25 Questions

Exercise 3.4 Solutions 9 Questions

Access Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

Prove that:

1.

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 1

Solution:

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 2

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 3

We get

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 4

= 0

= RHS

2. (sin 3+ sin x) sin + (cos 3– cos x) cos = 0

Solution:

Consider

LHS = (sin 3x + sin x) sin x + (cos 3x – cos x) cos x

By further calculation

= sin 3x sin x + sin2 x + cos 3x cos x – cos2 x

Taking out the common terms

= cos 3x cos x + sin 3x sin x – (cos2 x – sin2 x)

Using the formula

cos (A – B) = cos A cos B + sin A sin B

= cos (3x – x) – cos 2x

So we get

= cos 2x – cos 2x

= 0

= RHS

3.

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 5

Solution:

Consider

LHS = (cos x + cos y) 2 + (sin x – sin y) 2

By expanding using formula we get

= cos2 x + cos2 y + 2 cos x cos y + sin2 x + sin2 y – 2 sin x sin y

Grouping the terms

= (cos2 x + sin2 x) + (cos2 y + sin2 y) + 2 (cos x cos y – sin x sin y)

Using the formula cos (A + B) = (cos A cos B – sin A sin B)

= 1 + 1 + 2 cos (x + y)

By further calculation

= 2 + 2 cos (x + y)

Taking 2 as common

= 2 [1 + cos (x + y)]

From the formula cos 2A = 2 cos2 A – 1

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 6

4.

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 7

Solution:

LHS = (cos x – cos y) 2 + (sin x – sin y) 2

By expanding using formula

= cos2 x + cos2 y – 2 cos x cos y + sin2 x + sin2 y – 2 sin x sin y

Grouping the terms

= (cos2 x + sin2 x) + (cos2 y + sin2 y) – 2 (cos x cos y + sin x sin y)

Using the formula cos (A – B) = cos A cos B + sin A sin B

= 1 + 1 – 2 [cos (x – y)]

By further calculation

= 2 [1 – cos (x – y)]

From formula cos 2A = 1 – 2 sin2 A

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 8

5. sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

Solution:

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 9

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 10

6.

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 11

Solution:

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 12

7.

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 13

Solution:

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 14

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Find sin x/2, cos x/2 and tan x/2 in each of the following:

8.

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 17

Solution:

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 18

cos x = -3/5

From the formula

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 19

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 20

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 21

9. cos x = -1/3, x in quadrant III

Solution:

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 22

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10. sin x = 1/4, x in quadrant II

Solution:

NCERT Solutions for Class 11 Chapter 3 Miscellaneous Ex Image 25

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