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

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