Let P be the relation defined on the set of all real numbers such that P = a , b : sec 2 a - tan 2 b = 1 . Then, P is

Step-by-step solution

P = a , b : sec 2 a - tan 2 b = 1 P = a , a : sec 2 a - tan 2 a = 1 its reflexive relation. Now P = a , b : sec 2 a - tan 2 b = 1 sec 2 a - tan 2 b = 1 ⇒ sec 2 a = 1 + tan 2 b ⇒ sec 2 a = sec 2 b ⇒ sec   a = sec   b sec 2 a - tan 2 b = 1 1 + tan 2 a - sec 2 b + 1 = 1 sec 2 b - tan 2 a = 1 Hence, it is symmetric. If sec   a = sec   b and sec   b = sec   c then sec   a = sec   c ⇒ transitive So, it is an equivalence relation.