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

Question

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, reflexive and symmetric but not transitive, symmetric and transitive but not reflexive, reflexive and transitive but not symmetric, an equivalence relation

MARKS App · Accepted Answer

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.

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