Ask Me Help Desk - Help verify this trig identity? (cscB/sinB)-(cotB/tanB) = 1

I can see why you're having such difficulty! It's not a true statement. If you rewrite everything in terms of sines and cosines (which is always a good first step when trying to prove trig identities), you get the following:

$\frac{\csc B}{\sin B}-\frac{\cot B}{\tan B}=1$

$\frac{\frac{1}{\sin B}}{\sin B}-\frac{\frac{\cos B}{\sin B}}{\frac{\sin B}{\cos B}}=1$

$\frac{1}{\sin^2 B}-1=1$

$\frac{1}{\sin^2 B}=2$

That's only true when $B=\frac{\pi}{4}$ or $B=\frac{3\pi}{4}$ . That does not a trig identity make!