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Question: Range of \(f ( x ) = \sqrt { \ell n ( \cos ( \sin x ) ) }\) is...

Range of f(x)=ℓn(cos⁡(sin⁡x))f ( x ) = \sqrt { \ell n ( \cos ( \sin x ) ) } is

A

[0, ln (cosec 1))

B

[0, ln (sec 1))

C

(ln (cosec 1)), ln (sec 1))

D

{0}

Answer

{0}

Explanation

Solution

First of all we must ensure that ln (cos(sinx)) ≥ 0

⇒ cos(sinx) ≥ 1

⇒ cos(sinx) = 1 ⇒ ln cos(sinx) = 0

∀ x ∈ domain. Thus range is {0}.