How do you prove csctheta/sintheta=csc^2theta?

Oct 7, 2016

Easy! Just remember that $\frac{1}{\sin} \theta = \csc \theta$ and you will find that $\csc \frac{\theta}{\sin} \theta = {\csc}^{2} \theta$

Explanation:

To prove that $\csc \frac{\theta}{\sin} \theta = {\csc}^{2} \theta$, we have to remember that $\csc \theta = \frac{1}{\sin} \theta$

Proof: $\csc \frac{\theta}{\sin} \theta = {\csc}^{2} \theta$

$\frac{\frac{1}{\sin} \theta}{\sin} \theta = {\csc}^{2} \theta$

$\frac{1}{\sin} \theta \cdot \frac{1}{\sin} \theta = {\csc}^{2} \theta$

$\frac{1}{\sin} ^ 2 \theta = {\csc}^{2} \theta$
So, ${\csc}^{2} \theta = {\csc}^{2}$

There you go :)