# How do you prove (cos^2x) / (sin^2x) * (1) / cos^2x = csc^2x?

Apr 19, 2015

Know that:

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

So...

$L H S = {\cos}^{2} \frac{x}{\sin} ^ 2 x \cdot \frac{1}{\cos} ^ 2 x = \frac{1}{\sin} ^ 2 x = {\csc}^{2} x = R H S$

Apr 19, 2015

On the left hand side the ${\cos}^{2} x$ cancels out and you are
left with

$\frac{1}{\sin} ^ 2 x$

Now $\csc x = \frac{1}{\sin} x$

So

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