MHB 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.
[math]\frac{sec( \theta )}{tan( \theta )} = \frac{ \frac{1}{cos( \theta )}}{ \frac{sin( \theta )}{cos( \theta )}}[/math]

[math]= \frac{ \frac{1}{cos( \theta )}}{ \frac{sin( \theta )}{cos( \theta )}} \cdot \frac{ cos( \theta )}{cos( \theta )}[/math]

[math]= \frac{1}{sin( \theta )} = csc( \theta )[/math]

With, of course, the restrictions that [math]sin( \theta ) \neq 0[/math] and [math]cos( \theta ) \neq 0[/math]

-Dan