First, let's look at the trigonometric ratios;
[tex]\sin \Theta=\frac{opposite}{hypotenuse}[/tex][tex]\cos \Theta=\frac{adjacent}{hypoteunse}[/tex][tex]\tan \Theta=\frac{opposite}{adjacent}[/tex]
Let's check each option and see if it is true
A.
[tex]\sec \Theta=\frac{1}{\cos \Theta}[/tex][tex]=\frac{1}{\frac{adjacent}{\text{hypotenuse}}}[/tex][tex]=\frac{hypotenuse}{\text{adjacent}}[/tex]
option A is not true
B
[tex]\csc \Theta=\frac{1}{\sin \Theta}[/tex][tex]=\frac{1}{\frac{opposite}{\text{hypotenuse}}}[/tex][tex]=\frac{hypotenuse}{\text{opposite}}[/tex]
option B is also not true
Option C is correct because
[tex]\sec \Theta=\frac{hypotenuse}{adjacent}[/tex]
D
[tex]\cot \Theta=\frac{1}{\tan \Theta}[/tex][tex]=\frac{1}{\frac{opposite}{\text{adjacent}}}[/tex][tex]=\frac{adjacent}{\text{opposite}}[/tex]
option D is not true
Hence, only option C is true
