Answer:
The correct answer is a) [tex] \sec(x) = \sqrt{2}[/tex].
Step-by-step explanation:
Here we need to use some trigonometric identities:
- [tex] \csc(x) = \frac{1}{\sin(x)}[/tex],
- [tex] \cot(x) = \frac{\cos(x)}{\sin(x)} [/tex].
Then, substituting the above identities in the given formula we have:
[tex] \frac{\csc(x)}{\cot(x)} = \frac{\frac{1}{\sin(x)}}{\frac{\cos(x)}{\sin(x)}} = \frac{1}{\sin(x)}\frac{\sin(x)}{\cos(x)} [/tex]
Notice that we can simplify the sinus in both fractions. Thus,
[tex]\frac{\csc(x)}{\cot(x)} = \frac{1}{\cos(x)} = \sec{x}[/tex].
From here, the solutions is pretty straightforward.
