Differentiation Class 12 | Inverse Trigonometric Functions | intervals | class 12 maths | Rd Sharma

Differentiation of inverse trigonometric functions and use of intervals in such questions
You will be able to understand the concept of use or to solve intervals in such questions easily.

sin^-1(sinx)
a) -π-x, if x [-3π/2, -π/2]
b) x , if x [-π/2, π/2]
c) π-x, if x[π/2, 3π/2]
d) -2π+x, if [3π/2, 5π/2]

cos^-1(cosx)
a) -x, if x [-π, 0]
b) x , if x [0, π]
c) 2π-x, if x[π, 2/π]
d) -2π+x, if [2π, 3/π]

tan^-1(tanx)
a) π-x, if x (-3π/2, -π/2)
b) x , if x (-π/2, π/2)
c) π-x, if x(π/2, 3π/2)
d) -2π+x, if (3π/2, 5π/2)

Expression. Substitution
1. a²+x² x= atan@ or acot@
2. a²-x². x= asin@ or acos@
3. x²-a². x= asec@ or acosec@
4.√(a-x)/(a+x). x= acos2@
or √(a+x)/(a-x)
5.√(a²-x²)/(a²+x²) x²=a²cos2@
or √(a²+x²)/(a²-x²)

links of different chapter's

Chapter 23 to Chapter 27 Algebra of vectors | dot product | cross product | scalar triple product | direction cosines and direction ratios

Chapter 22 DIFFERENTIAL EQUATIONS

Chapter 9 and 10
Continuity and diffrentiability

Chapter 4 INVERSE TRIGNOMETRIC FUNCTIONS

Chapter 1 ,2 Relation And Function

Chapter 28 Straight Line In Space

Chapter 29 The Plane

Chapter 11 Differentiation

Chapter 19 Indefinite Integral

Chapter 20 Definite Integration

Chapter 5,6,7 and 8 algebra of matrices , determinant , adjoint and inverse of matrix and simultaneous linear equation

Chapter 14 to chapter 18 Application Of Derivative

Chapter 30 to chapter 32 probability , random variables and binomial distribution

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