# RD Sharma Solutions For Class 12 Maths Exercise 4.6 Chapter 4 Inverse Trigonometric Functions

RD Sharma Solutions Class 12 MathsÂ Exercise 4.6 Chapter 4 Inverse Trigonometric Functions is provided here. Students can make use of solutions PDF while solving exercise wise problems understanding the other possible ways of obtaining answers easily. The solutions are designed by subject matter experts based on the grasping abilities of students. It improves logical thinking skills among students, which are important from the exam point of view.

This exercise is completely based on the inverse of cotangent function. Students who aim to clear the exam with good marks can use RD Sharma Solutions Class 12 Maths Chapter 4 Inverse Trigonometric Functions Exercise 4.6 PDF as a reference guide to boost their exam preparation.

## Download the PDF of RD Sharma Solutions For Class 12 Chapter 4 – Inverse Trigonometric Functions Exercise 4.6

### Exercise 4.6 Page No: 4.24

1. Find the principal values of each of the following:

(i) cot-1(-âˆš3)

(ii) Cot-1(âˆš3)

(iii) cot-1(-1/âˆš3)

(iv) cot-1(tan 3Ï€/4)

Solution:

(i) Given cot-1(-âˆš3)

Let y = cot-1(-âˆš3)

– Cot (Ï€/6) = âˆš3

= Cot (Ï€ â€“ Ï€/6)

= cot (5Ï€/6)

The range of principal value of cot-1 is (0, Ï€) and cot (5 Ï€/6) = – âˆš3

Thus, the principal value of cot-1 (- âˆš3) is 5Ï€/6

(ii) Given Cot-1(âˆš3)

Let y = cot-1(âˆš3)

Cot (Ï€/6) = âˆš3

The range of principal value of cot-1 is (0, Ï€) and

Thus, the principal value of cot-1 (âˆš3) is Ï€/6

(iii) Given cot-1(-1/âˆš3)

Let y = cot-1(-1/âˆš3)

Cot y = (-1/âˆš3)

– Cot (Ï€/3) = 1/âˆš3

= Cot (Ï€ â€“ Ï€/3)

= cot (2Ï€/3)

The range of principal value of cot-1(0, Ï€) and cot (2Ï€/3) = – 1/âˆš3

Therefore the principal value of cot-1(-1/âˆš3) is 2Ï€/3

(iv) Given cot-1(tan 3Ï€/4)

But we know that tan 3Ï€/4 = -1

By substituting this value in cot-1(tan 3Ï€/4) we get

Cot-1(-1)

Now, let y = cot-1(-1)

Cot y = (-1)

– Cot (Ï€/4) = 1

= Cot (Ï€ â€“ Ï€/4)

= cot (3Ï€/4)

The range of principal value of cot-1(0, Ï€) and cot (3Ï€/4) = – 1

Therefore the principal value of cot-1(tan 3Ï€/4) is 3Ï€/4

### Access other exercises of RD Sharma Solutions For Class 12 Chapter 4 – Inverse Trigonometric Functions

Exercise 4.1 Solutions

Exercise 4.2 Solutions

Exercise 4.3 Solutions

Exercise 4.4 Solutions

Exercise 4.5 Solutions

Exercise 4.7 Solutions

Exercise 4.8 Solutions

Exercise 4.9 Solutions

Exercise 4.10 Solutions

Exercise 4.11 Solutions

Exercise 4.12 Solutions

Exercise 4.13 Solutions

Exercise 4.14 Solutions