Question

Simplifying Trigonometric Expressions-

Simplify the trigonometric expression$\frac{\sec x-\cos x}{\tan x}$

Short answer

On simplifying expression we get $\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{x}$

Step-by-step solution

Step 1. Given information

A trigonometric expression as$\frac{\sec x-\cos x}{\tan x}$

Step 2.  Concept used

Here we will use trigonometric identities for simplifying given expression into simplest form. That simplest form will be answer.

Step 3. Calculation

Now, simplify $\frac{\sec x-\cos x}{\tan x}$using identities:

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