Answer:
C, [tex]cot^2(x)[/tex]
Step-by-step explanation:
To solve this problem, we should know that:
- [tex]csc(x)=\frac{1}{sin(x)}[/tex]
- [tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
- [tex]cot(x)=\frac{cos(x)}{sin(x)}[/tex]
We can simply by expanding the expression first:
[tex]\frac{cos(x)\frac{1}{sin(x)} }{\frac{sin(x)}{cos(x)} } =\\\\\frac{\frac{cos(x)}{sin(x)} }{\frac{sin(x)}{cos(x)} }=\\\\\frac{cos(x)}{sin(x)}*\frac{cos(x)}{sin(x)} =\\\\\frac{cos^2(x)}{sin^2(x)} =\\\\cot^2(x)[/tex]
(Note that both x and theta are variables that can be replaced. I used x because there is not a symbol for theta on here. Please keep that in mind.)
Therefore, the answer is C.
I hope this helps! Let me know if you have any questions :)
