RD Sharma Solutions Class 12 Chapter 4 Exercise 4.6 2022

RD Sharma Solutions Class 12 Chapter 4 Exercise 4.6: Students can utilise the solutions PDF to help them comprehend the various options for obtaining answers while addressing exercise wise questions. Subject matter experts create the RD Sharma Solutions depending on the students’ comprehension ability. It helps students enhance their logical thinking skills, which are important for exams. This exercise is entirely focused on the cotangent function’s inverse.

Students who want to do well on the exam can utilise RD Sharma Solutions Class 12 Maths Chapter 4 Inverse Trigonometric Functions Exercise 4.6 PDF as a study material to help them prepare.

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Download RD Sharma Solutions Class 12 Chapter 4 Exercise 4.6 Free PDF

RD Sharma Solutions Class 12 Chapter 4 Exercise 4.6

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 4 – Inverse Trigonometric Functions Exercise 4.6 Important Questions With Solution

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

(i) cot^-1(-√3)

(ii) Cot^-1(√3)

(iii) cot^-1(-1/√3)

(iv) cot^-1(tan 3π/4)

Solution:

(i) Given cot^-1(-√3)

Let y = cot^-1(-√3)

– Cot (π/6) = √3

= Cot (π – π/6)

= cot (5π/6)

The range of principal value of cot^-1 is (0, π) and cot (5 π/6) = – √3

Thus, the principal value of cot^-1 (- √3) is 5π/6

(ii) Given Cot^-1(√3)

Let y = cot^-1(√3)

Cot (π/6) = √3

The range of principal value of cot^-1 is (0, π) and

Thus, the principal value of cot^-1 (√3) is π/6

(iii) Given cot^-1(-1/√3)

Let y = cot^-1(-1/√3)

Cot y = (-1/√3)

– Cot (π/3) = 1/√3

= Cot (π – π/3)

= cot (2π/3)

The range of principal value of cot^-1(0, π) and cot (2π/3) = – 1/√3

Therefore the principal value of cot^-1(-1/√3) is 2π/3

(iv) Given cot^-1(tan 3π/4)

But we know that tan 3π/4 = -1

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

Cot^-1(-1)

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

Cot y = (-1)

– Cot (π/4) = 1

= Cot (π – π/4)

= cot (3π/4)

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

Therefore the principal value of cot^-1(tan 3π/4) is 3π/4

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There are a total of 9 questions in RD Sharma Solutions for Class 12 Maths Chapter 4 Exercise 4.6.

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RD Sharma Solutions For Class 12 Maths Exercise 4.6 Chapter 4 (Updated for 2021-22)