The domain of the function $$f(x)=$$$$cos$$−$$1$$⁡$$34+2sin$$⁡x is

Correct option is 1−π6+2nπ,π6+2nπ

Questions

The domain of the function $f (x) = \cos^{- 1} (\frac{3}{4 + 2 \sin x}) is$

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−π6+2nπ,π6+2nπ

−π6-2nπ,π6+2nπ

−π6+2nπ,π6-2nπ

−π6-2nπ,π6-2nπ

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detailed solution

Correct option is A

f (x) is defined if −1≤34+2sin⁡x≤1Since, 4 + 2 sin x > 0 for all real x, therefore34+2sin⁡x≤1⇒3≤4+2sin⁡x⇒sin⁡x≥−12 ⇒−π6+2nπ≤x≤π6+2nπ,n∈Z Domain of f=−π6+2nπ,π6+2nπ

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The domain of the function f(x)=cos−1⁡34+2sin⁡x is

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The domain of the function $f (x) = \cos^{- 1} (\frac{3}{4 + 2 \sin x}) is$