Question

Simplifying Trigonometric Expressions-

Write the trigonometric expression $\mathit{c}\mathit{o}\mathit{s}\mathit{t}\mathit{t}\mathit{a}\mathit{n}\mathit{t}$in terms of sine and cosine, and then simplify.

Short answer

On simplifying expression we get$\sin t$

Step-by-step solution

Step 1. Given information

A trigonometric expression as$\cos t\tan t$

Step 2. Concept used

Write the following expression in terms of sine and cosine first. After that, simplify it with the help of trigonometric identities.

Step 3. Calculation

Now, write $\cos t\tan t$in form of $sineand\cos ine$:

$\begin{array}{l}\tan t=\frac{\sin t}{\cos t}\\ \cos t=\cos t\end{array}$

$\begin{array}{l}\cos t\tan t=\cos t\times \frac{\sin t}{\cos t}\\ =\sin t\end{array}$