Study Materials: ncert solutions

Our ncert solutions for Exercise 3.3 Class 11 maths 3. Trigonometric Functions - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

Solutions ⇒ Class 11th ⇒ Mathematics ⇒ 3. Trigonometric Functions

Exercise 3.3 Class 11 maths 3. Trigonometric Functions - ncert solutions - Toppers Study

Topper Study classes prepares ncert solutions on practical base problems and comes out with the best result that helps the students and teachers as well as tutors and so many ecademic coaching classes that they need in practical life. Our ncert solutions for Exercise 3.3 Class 11 maths 3. Trigonometric Functions - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

Exercise 3.3 Class 11 maths 3. Trigonometric Functions - ncert solutions - Toppers Study

CBSE board students who preparing for class 11 ncert solutions maths and Mathematics solved exercise chapter 3. Trigonometric Functions available and this helps in upcoming exams 2022-2023.

You can Find Mathematics solution Class 11 Chapter 3. Trigonometric Functions

  • All Chapter review quick revision notes for chapter 3. Trigonometric Functions Class 11
  • NCERT Solutions And Textual questions Answers
  • Extra NCERT Book questions Answers
  • Importatnt key points with additional Assignment and questions bank solved.

NCERT Solutions do not only help you to cover your syllabus but also will give to textual support in exams 2022-2023 to complete exercise 3.3 maths class 11 chapter 3 in english medium. So revise and practice these all cbse study materials like class 11 maths chapter 3.3 in english ncert book. Also ensure to repractice all syllabus within time or before board exams for ncert class 11 maths ex 3.3 in english.

See all solutions for class 11 maths chapter 3 exercise 3 in english medium solved questions with answers.

Exercise 3.3 class 11 Mathematics Chapter 3. Trigonometric Functions

3. Trigonometric Functions

| Exercise 3.3 |

Exercise 3.3 Class 11 maths 3. Trigonometric Functions - ncert solutions - Toppers Study


Exercise 3.3


Q5.  Find the value of

          (i) sin 75°                     (ii) tan 15°

Solution:

(i) sin 75° = sin (45° + 30°)      [∵ sin(x + y) = sin x cos y + cos x sin y ]

                 = sin 45° cos 30°  + cos 45° sin 30°  

(ii) tan 15°

Solution:

(ii)  tan 15° = tan (45° - 30°)

Q10. sin(n + 1)x sin(n + 2)x + cos(n + 1)x cos(n + 2)x = cos x

Solution:

LHS = sin(n + 1)x sin(n + 2)x + cos(n + 1)x cos(n + 2)x

Or       cos(n + 2)x cos(n + 1)x + sin(n + 2)x sin(n + 1)x 

Let be the A = (n + 2)x, B = (n + 1)x

Now we have,

LHS = cos A cos B + sin A sin B    

       =  cos ( A - B)      [∵ sin(x + y) = sin x cos y + cos x sin y ]

       = cos [(n + 2)x - (n + 1)x]  

       = cos [nx + 2x - (nx + x) ]

       = cos [nx + 2x - nx - x ]

       = cos x

LHS = RHS 

Q12. sin2 6x - sin2 4x = sin 2x sin 10x

Solution:

Sin2 A - sin2B = sin(A + B) sin(A - B)

LHS = sin2 6x - sin2 4x

        = sin (6x + 4x) sin(6x - 4x)

        = sin 10x sin 2x

        = sin 2x sin 10x

LHS = RHS 

Q13. cos2 2x - cos2 6x = sin 4x sin 8x

Solution:

LHS = cos2 2x - cos2 6x

        = (1 - sin2 2x) - (1 - sin2 6x)

        = (1 - sin2 2x - 1 + sin2 6x)

        = - sin2 2x + sin2 6x

        = sin2 6x - sin2 2x

        = sin (6x + 2x) sin(6x -2x)

        = sin 10x sin 4x    

Q24. cos 4x = 1 – 8 sin2  x cos2 x

Solution:

LHS = cos 2(2x)

       = cos 2A   [ Let be A = 2x ]

       = 1 - 2 sin2 A

       = 1 - 2 sin2 2x    [Putting A = 2x ]

       = 1 - 2 [sin 2x]2

       = 1 - 2 [2 sin x cos x ]2

       = 1 - 2 [4 sin2 x cos2 x]

       = 1 - 8 sin2 x cos2 x

LHS = RHS 

Q25.  cos 6x = 32 cos6 x – 48cos4 x + 18 cos2 x – 1

Solution:

LHS = cos 6x  = cos 3(2x)

        = cos 3A    [Let be A = 2x]

        = 4 cos3 A - 3 cos A

        = 4 cos3 2x - 3 cos 2x    [Putting A = 2x]

        = 4 [cos 2x]3 - 3 [cos 2x]

        = 4 [2cos2 x – 1]3 - 3 [2cos2 x – 1]

        = 4 [(2cos2 x)3 - 13 - 3(2cos2 x)2 (1) + 3 (2cos2 x)(1)2  ] - 3 [2cos2 x – 1]

        = 4 [8 cos6 x - 1 - 12 cos2 x + 6 cos2 x] - 6 cos2 + 3

        = 32 cos6 x - 4 - 48 cos2 x + 24 cos2 x - 6 cos2 + 3

        = 32 cos6 x - 48 cos2 x + 18 cos2 x - 1

LHS = RHS 

 

 

Select Your CBSE Classes

Important Study materials for classes 06, 07, 08,09,10, 11 and 12. Like CBSE Notes, Notes for Science, Notes for maths, Notes for Social Science, Notes for Accountancy, Notes for Economics, Notes for political Science, Noes for History, Notes For Bussiness Study, Physical Educations, Sample Papers, Test Papers, Mock Test Papers, Support Materials and Books.

 

 

Mathematics Class - 11th

NCERT Maths book for CBSE Students.

books

Study Materials List:

Solutions ⇒ Class 11th ⇒ Mathematics
1. Sets
2. Relations and Functions
3. Trigonometric Functions
4. Principle Of Mathematical Induction
5. Complex Numbers and Quadratic Equations
6. Linear Inequalities
7. Permutations and Combinations
8. Binomial Theorem
9. Sequences and Series
10. Straight Lines
11. Conic Sections
12. Introduction to Three Dimensional Geometry
13. Limits and Derivatives
14. Mathematical Reasoning
15. Statistics
16. Probability

Topper's Study

New Books