Define a relation R on the interval $\left[0, \frac{\pi}{2}\right)$ by $x\mathrm{R}y$ if and only if $\sec^2 x - \tan^2 y = 1$. Then R is:\\
(1) both reflexive and transitive but not symmetric\\
(2) an equivalence relation\\
(3) reflexive but neither symmetric nor transitive\\
(4) both reflexive and symmetric but not transitive