Question

Simplifying Trigonometric Expressions-

Write the trigonometric expression $\frac{\mathbf{s}\mathbf{e}\mathbf{c}\mathbf{x}}{\mathbf{c}\mathbf{s}\mathbf{c}\mathbf{x}}$in terms of sine and cosine, and then simplify.

Short answer

On simplifying expression we get$\mathit{t}\mathit{a}\mathit{n}\mathit{x}$

Step-by-step solution

Step 1. Given information

A trigonometric expression as$\frac{\sec x}{\csc x}$

Step 2. Concept used

Begin by writing the expression in sine and cosine terms. Then use trigonometric identities to further decrease it.

Step 3. Calculation

Now, write $\frac{\sec x}{\csc x}$in form of $sineand\cos ine$:

$\begin{array}{l}\frac{\sec x}{\csc x}\\ =\frac{1}{\cos x}\times \sin x\\ =\frac{\sin x}{\cos x}\\ =\tan x\end{array}$