Question

Please explain how you prove this!!
(csc(x)-cot(x))(csc(x)+cot(x))=1

Answer 1

If you multiply out the two groups, you get:\[\csc^{2}x + \csc x \cot x - \csc x \cot x - \cot^{2}x = 1\]The cscxcotx's cancel, giving you\[\csc^{2}x - \cot^{2}x = 1\]Using the identity I showed you a moment ago (cot^2x + 1 = csc^2x), replace csc^2x\[(\cot^{2}x + 1) - \cot^{2}x = 1\]The cotangents cancel and you're left with \[1 = 1\]

Answer 2

Thank you, do you happen to know all the identities?