- #1
tmt1
- 230
- 0
I have $\frac{sec\theta}{tan\theta}$. How can I simplify it to get $\csc\left({\theta}\right)$ ?
MHB How Can $\frac{\sec\theta}{\tan\theta}$ Be Simplified to $\csc(\theta)$?
- Thread starter tmt1
- Start date
-
- Tags
- Simplifying Trig
Click For Summary
The expression $\frac{\sec\theta}{\tan\theta}$ can be simplified to $\csc(\theta)$ by converting secant and tangent into sine and cosine functions. This involves rewriting $\sec(\theta)$ as $\frac{1}{\cos(\theta)}$ and $\tan(\theta)$ as $\frac{\sin(\theta)}{\cos(\theta)}$. By performing the division, the equation simplifies to $\frac{1}{\sin(\theta)}$, which is equal to $\csc(\theta)$. It's important to note that this simplification is valid under the conditions that $\sin(\theta) \neq 0$ and $\cos(\theta) \neq 0$. Thus, $\frac{\sec\theta}{\tan\theta} = \csc(\theta)$ when these restrictions are met.