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$The domain of f (x) = \sqrt{\cos (\sin x)}$ is

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a

R

b

R+

c

R-

d

ϕ

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detailed solution

Correct option is A

f(x)=cos⁡(sin⁡x) is defined if cos⁡(sin⁡x)≥0----(1) As we know, −1≤sin⁡x≤1 for all x∈R . So, cos⁡θ≥0 (Here, θ=sin⁡x lies in the first and fourth quadrants) i.e., cos⁡(sin⁡x)≥0 for all x i.e., x∈R Thus, the domain of f(x) is R .

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