# Thread: Simplifying A trig equation

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

2. Originally Posted by tmt
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

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