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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

Options

  1. Areflexive and symmetric but not transitive
  2. Bsymmetric and transitive but not reflexive
  3. Creflexive and transitive but not symmetric
  4. Dan equivalence relation

Correct answer

D. an equivalence relation

Step-by-step solution

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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