Last updated at May 29, 2018 by Teachoo

Transcript

Ex 3.3, 23 Prove that tan 4 = (4 tan (1 tan2 ) )/(1 6 tan2 +tan4 ) Taking L.H.S. tan 4x = (2 tan 2x)/(1 tan2 2x) tan 4x = 2((2 tan )/(1 2 ))/(1 ((2 tan )/(1 2 ))^2 ) = (((4 tan )/(1 2 )))/(1 ((2 tan )^2/(1 2 )^2 ) ) = (((4 tan )/(1 2 )))/(1 ((4 ^2 )/(1 2 )^2 ) ) = (((4 tan )/(1 2 )))/((((1 2 )^2 4 ^2 )/(1 2 )^2 ) ) = (4 tan )/(1 tan2 ) ((1 tan2 )2 )/((1 2 )2 4 tan2 ) = (4 tan )/1 ((1 tan2 ) )/((1 2 )2 4 tan2 ) = (4 tan (1 2 ))/((1 tan2 )2 4 tan 2 ) Using (a b)2 = a2 +b2 2ab = (4 tan ( 1 tan2 ) )/(( (1)2+( 2 )2 2 1 2 ) 4 2 ) = (4 tan ( 1 tan2 ) )/(( (1)2+( 2 )2 2 1 2 ) 4 2 ) = (4 tan ( 1 tan2 ) )/(1 + tan 4 2 tan2 4 tan2 ) = (4 tan ( 1 tan2 ) )/(1 + tan4 6 4 ) = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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 You are here

Ex 3.3, 21 Important

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.