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