Question

Simplifying Trigonometric Expressions-

Write the trigonometric expression $\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }\mathit{s}\mathit{e}\mathit{c}\mathit{\theta }$in terms of sine and cosine, and then simplify.

Short answer

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

Step-by-step solution

Step 1. Given information

An trigonometric expression as$\sin \theta \sec \theta$

Step 2. Concept used

To begin, write the formula in sine and cosine terms. After that, reduce it using trigonometric identities.

Step 3. Calculation

Now, write $\sin \theta \sec \theta$in form of $sineand\cos ine$:

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