Question

simplify
cosxcscx/cot^2x

Answer 1

Question: Simplify

$$\cos x * \csc x / \cot^ {2} x.$$

Solution. To simplify the expression, let us recall the definition of cosecant and cotangent functions:

$$\csc x = \frac {1}{\sin x},$$ $$\cot x = \frac {\cos x}{\sin x}.$$

We now substitute these functions with the expressions on the right, step by step.

First, replace $\cot x$ in the denominator with the appropriate formula:

$$\frac {\cos x * \csc x}{\cot^ {2} x} = \frac {\cos x * \csc x}{\frac {\cos^ {2} x}{\sin^ {2} x}} = \frac {\cos x * \csc x * \sin^ {2} x}{\cos^ {2} x} = \frac {\csc x * \sin^ {2} x}{\cos x}.$$

We will now utilize the definition of $\csc x$:

$$\frac {\csc x * \sin^ {2} x}{\cos x} = \frac {\frac {1}{\sin x} * \sin^ {2} x}{\cos x} = \frac {\sin x}{\cos x} = \tan x.$$

Answer.

$$\frac {\cos x * \csc x}{\cot^ {2} x} = \tan x.$$