How Can $\frac{\sec\theta}{\tan\theta}$ Be Simplified to $\csc(\theta)$?

[tmt1]

I have $\frac{sec\theta}{tan\theta}$. How can I simplify it to get $\csc\left({\theta}\right)$ ?

 

[topsquark]

I have $\frac{sec\theta}{tan\theta}$. How can I simplify it to get $\csc\left({\theta}\right)$ ?

I prefer to change everything to sines and cosines.
\(\displaystyle \frac{sec( \theta )}{tan( \theta )} = \frac{ \frac{1}{cos( \theta )}}{ \frac{sin( \theta )}{cos( \theta )}}\)

\(\displaystyle = \frac{ \frac{1}{cos( \theta )}}{ \frac{sin( \theta )}{cos( \theta )}} \cdot \frac{ cos( \theta )}{cos( \theta )}\)

\(\displaystyle = \frac{1}{sin( \theta )} = csc( \theta )\)

With, of course, the restrictions that \(\displaystyle sin( \theta ) \neq 0\) and \(\displaystyle cos( \theta ) \neq 0\)

-Dan