From $sin^2$(x) + $cos^2$(x) = 1: divide by $cos^2$(x) to get 1 + $tan^2$(x) = $sec^2$(x), divide by $sin^2$(x) to get 1 + $cot^2$(x) = $csc^2$(x). These three identities are the foundation for simplifying and proving all other identities. Always try these first when stuck.