RD Chapter 4 Inverse Trigonometric Functions Ex 4.2 Solutions
Question - 1 : - Find the domain of definition of f(x) = cos -1 (x2 –4)
Answer - 1 : -
Given f(x) = cos -1 (x2 –4)
We know that domain ofcos-1 (x2 – 4) lies in the interval [-1, 1]
Therefore, we canwrite as
-1 ≤ x2 –4 ≤ 1
4 – 1 ≤ x2 ≤1 + 4
3 ≤ x2 ≤5
±√ 3 ≤ x ≤ ±√5
– √5 ≤ x ≤ – √3 and √3≤ x ≤ √5
Therefore domain ofcos-1 (x2 – 4) is [- √5, – √3] ∪ [√3, √5]
Question - 2 : - Find the domain of f(x) = cos-1 2x + sin-1 x.
Answer - 2 : -
Given that f(x) = cos-1 2x+ sin-1 x.
Now we have to findthe domain of f(x),
We know that domain ofcos-1 x lies in the interval [-1, 1]
Also know that domainof sin-1 x lies in the interval [-1, 1]
Therefore, the domainof 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]
Question - 3 : - Find the domain of f(x) = cos-1x + cos x.
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Question - 4 : - 
Answer - 4 : - 
Question - 5 : - Find the principalvalue of each of the following :
Answer - 5 : -
Question - 6 : - Find the principalvalue of each of the following :
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Question - 7 : - 
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Question - 8 : - 
Answer - 8 : -