Chapter 13.9, Problem 3MRE

To determine

To prove: The given identity.

Explanation of Solution

Given information:

The identity is $\sec x-\sin x\tan x=\cos x$

Calculation:

Consider the equation.

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