Chapter 13.7, Problem 12MRE

To determine

To simplify: The given function.

Answer to Problem 12MRE

The simplification of the given function is $\sin x$ .

Explanation of Solution

Given:

The given function is,

  $\csc x-\cos x\cot x$

Calculation:

Solve the given function,

  $\begin{array}{c}\csc x-\cos x\cot x=\frac{1}{\sin x}-\cos x\frac{\cos x}{\sin x}\\ =\frac{1-{\cos }^{2}x}{\sin x}\\ =\frac{{\sin }^{2}x}{\sin x}\\ =\sin x\end{array}$

Thus, the simplification of the given function is $\sin x$ .