Question

Simplifying Trigonometric Expressions-

Simplify the trigonometric expression$\left(\frac{\sin x\sec x}{\tan x}\right)$

Short answer

On simplifying expression we get 1

Step-by-step solution

Step 1. Given information

A trigonometric expression as$\left(\frac{\sin x\sec x}{\tan x}\right)$

Step 2. Concept used

We'll need to apply trigonometric identities to simplify the expression. We'll simplify it and give you our response.

Step 3. Calculation

Now, simplify $\left(\frac{\sin x\sec x}{\tan x}\right)$using identities:

$\begin{array}{l}\left(\tan x=\frac{\sin x}{\cos x}\right)\&\\ \left(\sec x=\frac{1}{\cos x}\right)\\ \frac{\sin x\times \sec x}{\tan x}=\frac{\sin x\times \frac{1}{\cos x}}{\frac{\sin x}{\cos x}}\\ \frac{\sin x\times \sec x}{\tan x}=1\end{array}$