Question

simplify.
\csc x cot x
use algebra and the fundamental trigonometric identities.
your answer should be a number or use a single trigonometric function.

Explanation:

Step1: Substitute the identity for \(\csc x\)

We know that \(\csc x=\frac{1}{\sin x}\). So, \(\csc x\cos x=\frac{1}{\sin x}\cdot\cos x\).

Step2: Simplify the expression

Using the rule of fraction - multiplication \(\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}\), here \(a = 1\), \(b=\sin x\), \(c=\cos x\), \(d = 1\). Then \(\frac{1}{\sin x}\cdot\cos x=\frac{\cos x}{\sin x}\).
Since \(\frac{\cos x}{\sin x}=\cot x\) (by the quotient identity \(\cot x=\frac{\cos x}{\sin x}\)).

Answer:

\(\cot x\)