Let $P$ be the relation defined on the set of all real numbers such that $P = \left\{ ( a , b ) : \sec ^ { 2 } a - \tan ^ { 2 } b = 1 \right\}$. Then, $P$ is\\
(1) reflexive and symmetric but not transitive\\
(2) symmetric and transitive but not reflexive\\
(3) reflexive and transitive but not symmetric\\
(4) an equivalence relation