Find the principal value of each of the following:

RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12^th

Q. No. 4 of Exercise 4.2

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4

Find the principal value of each of the following:

Let .

Then, cos y =

= –cos

= cos

= cos

We know that the range of the principal value branch of is [0,] and cos

Therefore, the principal value of is .

4

Chapter Exercises

Exercise 4.1

Exercise 4.2

Exercise 4.3

Exercise 4.4

Exercise 4.5

Exercise 4.6

Exercise 4.7

Exercise 4.8

Exercise 4.9

Exercise 4.10

Exercise 4.11

Exercise 4.12

Exercise 4.13

Exercise 4.14

Very short answer

MCQ

1

Find the domain of definition of f(x) = cos^–1(x²–4).

2

Find the domain of f(x) = cos^–12x + sin^–1x.

3

Find the domain of f(x) = cos^–1 x + cos x.

4

Find the principal value of each of the following:

4

Find the principal value of each of the following:

4

Find the principal value of each of the following:

4

Find the principal value of each of the following:

5

For the principal values, evaluate each of the following:

5

For the principal values, evaluate each of the following:

5

For the principal values, evaluate each of the following:

5

For the principal values, evaluate each of the following: