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antoniarose · Sep 5, 2011, 01:17 PM

I have tried so many times to verify this identity but I can't do it! If you have any ideas, please let me know, and if you know how to do it, the steps would be greatly appreciated! Thank you! Please help!

(cscB/sinB)-(cotB/tanB) = 1

jcaron2 · Sep 5, 2011, 08:06 PM

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!