Answer:
sec x
Step-by-step explanation:
Let's set each function equal to zero to see if they have zero in their function.
If there is no solution, then we no solution of zero.
[tex] \cos(x) = 0[/tex]
[tex]x = \frac{\pi}{2} + 2\pi(n)[/tex]
So there is a solution of zero.
[tex] \cot(x) = 0[/tex]
[tex] \frac{ \cos(x) }{ \sin(x) } = 0[/tex]
There answer here is
[tex]x = \frac{\pi}{2} + 2\pi(n)[/tex]
So there is a solution. of zero here
If cot x=0, has a solution of zero, then tan x does as well. Since we can use
[tex] \frac{ \sin(x) }{ \cos(x) } = \tan(x) [/tex]
[tex] \frac{ \sin(x) }{ \cos(x) } = 0[/tex]
The answer here will be
[tex]0 + 2\pi(n)[/tex]
So that leaves sec x.
Proof:
[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]
1 divided by any number won't equal zero, so the solution will never be 0.
