ANSWER
[tex] \sec(x) = \frac{ \sqrt{3} }{4} [/tex]
EXPLANATION
The correct answer is option D.
The value of the basic cosine function is between negative one and one.
That is for
[tex]f(x)= \cos(x) [/tex]
the range of f is
[tex][-1,1][/tex]
The given equation in option D is
[tex] \sec(x) = \frac{ \sqrt{3} }{4} [/tex]
We know that the secant function is the reciprocal of the cosine function.
This implies that,
[tex] \cos(x) = \frac{4}{ \sqrt{3} } = \frac{4 \sqrt{3} }{3} [/tex]
This value is more than 1. It is not within the range of the cosine function, hence it is false because it is not defined.
