Answer:
The correct choice is D
Step-by-step explanation:
The trigonometric functions, [tex]\sin x[/tex] and [tex]\cos x[/tex] are defined for all real numbers.
[tex]\tan x=\frac{\sin x}{\cos (x)}[/tex], this function is not defined where [tex]\cos x=0[/tex].
[tex]\cot x=\frac{\cos x}{\sin (x)}[/tex], this function is not defined where [tex]\sin x=0[/tex].
[tex]\csc x=\frac{1}{\sin (x)}[/tex], this function is not defined where [tex]\sin x=0[/tex].
For option A
The domain of [tex]f(x)=\sin(x)[/tex] is all real numbers.
The domain of g(x) =tanx is [tex]x\ne \frac{(2n+1)\pi}{2}[/tex]
For option B
The domain of [tex]f(x)=\cos(x)[/tex] is all real numbers.
The domain of f(x) =csc(x) is [tex]x\ne n\pi[/tex]
For option C,
The domain of G(x) =tanx is [tex]x\ne \frac{(2n+1)\pi}{2}[/tex]
The domain of f(x) =cot(x) is [tex]x\ne n\pi[/tex]
For option D;
The domain of f(x) =cot(x) is [tex]x\ne n\pi[/tex]
The domain of f(x) =csc(x) is [tex]x\ne n\pi[/tex]
Using it's concept, it is found that the functions that have the same domain are given by:
D. F(x) = cot x and f(x) = csc x
It is the set that contains all possible input values. In a fraction, for example, the denominator cannot be zero.
In this problem, we have that:
[tex]\cot{x} = \frac{\cos{x}}{\sin{x}}[/tex]
[tex]\csc{x} = \frac{1}{\sin{x}}[/tex]
That is, in both functions, the domain is all values of x except those for which [tex]\sin{x} = 0[/tex], hence option D is correct.
More can be learned about the domain of a function at https://brainly.com/question/25897115
