RD Sharma Solutions Class 12 Maths Exercise 4.2 Chapter 4 Inverse Trigonometric Functions are provided here. This exercise covers the problems based on the inverse of the cosine functions. These problems are solved in the best possible way to improve logical thinking skills among students. The faculty has vast experience in their respective field design solutions relevant to the exam pattern.
The RD Sharma Solutions contain explanations in a comprehensive manner to make it interesting for the students while solving. To score good marks in the exam, students can refer to RD Sharma Solutions Class 12 Maths Chapter 4 Inverse Trigonometric Functions Exercise 4.2, which are available here.
RD Sharma Solutions for Class 12 Chapter 4 – Inverse Trigonometric Functions Exercise 4.2
Access answers to Maths RD Sharma Solutions for Class 12 Chapter 4 – Inverse Trigonometric Functions Exercise 4.2
Exercise 4.2 Page No: 4.10
1. Find the domain of definition of f(x) = cos -1 (x2 – 4)
Solution:
Given f(x) = cos -1 (x2 – 4)
We know that the domain of cos-1 (x2 – 4) lies in the interval [-1, 1]
Therefore, we can write as
-1 ≤ x2 – 4 ≤ 1
4 – 1 ≤ x2 ≤ 1 + 4
3 ≤ x2 ≤ 5
±√ 3 ≤ x ≤ ±√5
– √5 ≤ x ≤ – √3 and √3 ≤ x ≤ √5
Therefore, the domain of cos-1 (x2 – 4) is [- √5, – √3] ∪ [√3, √5]
2. Find the domain of f(x) = cos-1 2x + sin-1 x.
Solution:
Given that f(x) = cos-1 2x + sin-1 x.
Now we have to find the domain of f(x).
We know that the domain of cos-1 x lies in the interval [-1, 1]
Also, know that the domain of sin-1 x lies in the interval [-1, 1]
Therefore, the domain of cos-1 (2x) lies in the interval [-1, 1]
Hence, we can write as,
-1 ≤ 2x ≤ 1
– ½ ≤ x ≤ ½
Hence, domain of cos-1(2x) + sin-1 x lies in the interval [- ½, ½]
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