Last updated at March 11, 2017 by Teachoo

Transcript

Example 5 Express tan-1 cosx/(1 − sinx ) , - π/2 < x < 3π/2 in the simplest form Lets first calculate cos x & 1 – sin x Solving tan-1 (cosx/(1 〖− sin〗x )) = tan-1 [(cos2 x/2 − sin2 x/2)/(1 − (2 〖sin 〗〖x/2 cos〖 x/2〗 〗 ) )] = tan-1 [(cos2 x/2 − sin2 x/2)/(1 − 2 〖sin 〗〖x/2 〖 cos 〗〖x/2〗 〗 )] = tan-1 [(cos2 x/2 − sin2 x/2)/(cos2 x/2 + sin2 x/2 − 2 〖sin 〗〖x/2 cos〖 x/2〗 〗 )] = tan-1 [(cos x/2 + sin x/2)(cos x/2 − sin x/2)/(cos x/2 − sin x/2)^2 ] = tan-1 [((cos x/2 + sin x/2))/((cos x/2 − sin x/2) )] Dividing by cos 𝑥/2 = tan-1 ((cos〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 + sin〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 )/(𝑐𝑜𝑠〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 − 𝑠𝑖𝑛〖 𝑥/( 2 )〗/〖𝑐𝑜𝑠 〗〖 𝑥/2〗 )) = tan-1 [(1 + 〖tan 〗〖𝑥/2〗)/(1 − tan〖 𝑥/2〗 )] = tan-1 [(1 + 〖tan 〗〖𝑥/2〗)/(1 − 〖1. tan〗〖 𝑥/2〗 )] = tan-1 ((𝑡𝑎𝑛〖 𝜋/4〗 + 〖𝑡𝑎𝑛 〗〖𝑥/2〗)/( 1− 〖𝑡𝑎𝑛 〗〖𝜋/4 〗.〖 𝑡𝑎𝑛 〗〖𝑥/2〗 )) = tan -1 [tan(π/4+x/2 ) ] = π/4+x/2

Ex 2.1, 5
Important

Ex 2.1, 8 Important

Ex 2.1, 12 Important

Ex 2.1, 14 Important

Example 5 Important You are here

Example 8 Important

Ex 2.2, 12 Important

Ex 2.2, 15 Important

Ex 2.2, 19 Important

Ex 2.2, 21 Important

Example 10 Important

Example 12 Important

Example 13 Important

Misc. 2 Important

Misc. 7 Important

Misc. 10 Important

Misc. 11 Important

Misc 12 Important

Misc. 17 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.