P={(a,b):sec2a−tan2b=1} For reflexive : sec2a−tan2a=1( true ∀a) For symmetric : sec2b−tan2a=1 L.H.S 1+tan2b−(sec2a−1)=1+tan2b−sec2a+1 =−(sec2a−tan2b)+2 =−1+2=1 So, Relation is symmetric For transitive : if sec2a−tan2b=1 and sec2b−tan2c=1 sec2a−tan2c=(1+tan2b)−(sec2b−1) =−sec2b+tan2b+2 =−1+2=1 So, Relation is transitive. Hence, Relation P is an equivalence relation