Class 11 Maths Ncert Trigonometry Supplementary Exercise Solutions
Chapter 3 Trigonometric Functions of Class 11 Maths is categorized under the term – II CBSE Syllabus for 2021-22. The miscellaneous exercise contains questions covering the entire topics present in the chapter. The last exercise of NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions is based on the following topics:
- Angles
- Trigonometric Functions
- Trigonometric Functions of Sum and Difference of Two Angles
- Trigonometric Equations
The solutions provided here are based on the latest guidelines of term – II prescribed by the CBSE. The NCERT Solutions for Class 11 can help the students in preparing well for the second term examination.
Download PDF of NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Miscellaneous Exercise
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.
Solution:
We get
= 0
= RHS
2. (sin 3x+ sinx) sinx+ (cos 3x– cosx) cosx= 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.
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
4.
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
5. sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x
Solution:
6.
Solution:
7.
Solution:
8. Find sin x/2, cos x/2 and tan x/2 in each of the following:
Solution:
cos x = -3/5
From the formula
9. cos x = -1/3, x in quadrant III
Solution:
10. sin x = 1/4, x in quadrant II
Solution:
Class 11 Maths NCERT supplementary or miscellaneous exercise solutions pdfs are provided here.
Class 11 Maths Ncert Trigonometry Supplementary Exercise Solutions
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