Question

Simplifying Trigonometric Expressions-

Write the trigonometric expression $\frac{\mathbf{c}\mathbf{o}\mathbf{t}\mathbf{\theta }}{\mathbf{cosec}\mathbf{\theta }\mathbf{-}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\theta }}$in terms of sine and cosine, and then simplify.

Short answer

On simplifying expression we get$\frac{\mathbf{1}}{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }}$

Step-by-step solution

Step 1. Given information

A trigonometric expression as$\frac{\cot \theta }{\mathrm{cosec}\theta -\sin \theta }$

Step 2. Concept used

We must apply trigonometric identities to simplify the following equation. We'll reduce it to its most basic form, and that will be our response.

Step 3. Calculation

Now, write$\frac{\cot \theta }{\mathrm{cosec}\theta -\sin \theta }$ in form of $sineand\cos ine$:

Formula used and further calculation-