Last updated at May 29, 2018 by Teachoo

Transcript

Ex3.3, 21 Prove that (cos4𝑥 + cos3𝑥 + cos2𝑥)/(sin4𝑥 + sin3𝑥 + sin2𝑥 ) = cot 3x Taking L.H.S Solving Numerator and Denominator separately We know that cos x + cos y = 2cos ((𝑥 + 𝑦)/2) cos ((𝑥 −.𝑦)/2) Replacing x by 4x and y by 2x cos 4x + cos 2x = 2cos ((4𝑥 + 2𝑥)/2). cos ((4𝑥 − 2𝑥)/2) = 2cos (6𝑥/2). cos (2𝑥/2) = 2 cos 3x . cos x Now cos 4x + cos 2x + cos 3x = 2cos 3x . cos x + cos 3x = cos 3x ( 2cos x + 1 ) Similarly, Solving denominator sin 4x + sin 2x + sin 3x We know that sin x + sin y = 2sin ((𝑥 + 𝑦)/2) sin ((𝑥 −𝑦)/2) Replacing x by 4x and y by 2x sin 4x + sin 2x = 2 sin ((4𝑥 +2𝑥)/2). cos ((4𝑥 − 2𝑥)/2) = 2 sin (6𝑥/2). cos (2𝑥/2) = 2 sin 3x . cos x Now, sin 4x + sin 2x + sin 3x = sin 4x + sin 2x + sin 3x = 2sin 3x . cos x + sin 3x = sin 3x (2cos x + 1) Hence (cos4𝑥 + cos3𝑥 + cos2𝑥)/(sin4𝑥 + sin3𝑥 + sin2𝑥 ) = (cos3𝑥 (2 𝑐𝑜𝑠 𝑥 +1 ))/(sin3𝑥 (2 𝑐𝑜𝑠 𝑥 +1 )) = cos3𝑥/sin3𝑥 = cot 3x = R.H.S. Hence R.H.S. = L.H.S. Hence proved

Chapter 3 Class 11 Trigonometric Functions

Ex 3.1, 1
Important

Ex 3.1, 2 Important

Ex 3.2, 7 Important

Ex 3.2, 8 Important

Ex 3.2, 9 Important

Ex 3.3, 4 Important

Ex 3.3, 5 Important

Ex 3.3, 8 Important

Ex 3.3, 11 Important

Ex 3.3, 18 Important

Ex 3.3, 23 Important

Ex 3.3, 21 Important You are here

Example 24 Important

Ex 3.4, 4 Important

Ex 3.4, 8 Important

Ex 3.4, 9 Important

Example 27 Important

Example 28 Important

Misc 4 Important

Misc 7 Important

Class 11

Important Question for exams Class 11

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.