Question

Hi, I need help with this problem please. No explanations/steps required. Just need the final answer

Answer 1

To simplify the expression we fist need to express each trigonometric function in terms of sines and cosines; to do this we need to remember that:

$\begin{gathered} \sec x=\frac{1}{\cos x} \\ \csc x=\frac{1}{\sin x} \end{gathered}$

With this in mind we have:

$\begin{gathered} \frac{\csc x}{\sec x}=\frac{\frac{1}{\sin x}}{\frac{1}{\cos x}} \\ =\frac{\cos x}{\sin x} \end{gathered}$

Finally we need to remember that:

$\cot x=\frac{\cos x}{\sin x}$

Therefore, we have that:

$\frac{\csc x}{\sec x}=\cot x$