Question

How to verify the following identitie:cot(-t)+tan(-t)/cot(t)=-sec^2t

Answer 1

\[\frac{ -\cot(t)-tant }{ \cot(t) }=\frac{- \frac{ cost }{ sint }-\frac{ sint }{cost } }{ \frac{ cost }{sint } }=-\frac{ \frac{ \cos ^{2}t+\sin ^{2}t }{sintcost } }{ \frac{ cost }{ sint }}\]
\[-\frac{ 1 }{sint cost }.\frac{ sint }{ cost }=-\frac{ 1 }{\cos ^{2}t }=-\sec ^{2}t\]

Answer 2

proof is completed