this is a trigonomic identity, but im unsure how to verify it
1+1/tan(x)=1/sin(x)
Are you sure this works out?
Take the case where $\displaystyle \displaystyle x = \frac{\pi}{4}$
$\displaystyle \displaystyle 1+ \frac{1}{\tan \left( \frac{\pi}{4}\right)} = 1+\frac{1}{1} = 2$
$\displaystyle \displaystyle \frac{1}{\sin \left(\frac{\pi}{4}\right)}= \frac{1}{\frac{1}{\sqrt{2}}} = \sqrt{2}$