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

Sets, Relations and Function: Let P be the relation defined on the set of all real numbers such… | JEE Main 2014

JEE Main 2014 (Online) 9th AprilQuestion 1

Let $P$ be the relation defined on the set of all real numbers such that $P=\left\{(a,b):\sec^{2}a-\tan^{2}b=1\right\}$. Then, $P$ is

Sets, Relations and Function

reflexive and symmetric but not transitivesymmetric and transitive but not reflexivereflexive and transitive but not symmetrican equivalence relation✓ Correct answer

Solution

$\sec^2a-\tan^2b=1\iff1+\tan^2a-\tan^2b=1\iff\tan^2a=\tan^2b$, which is an equality-type relation, hence reflexive, symmetric and transitive: an equivalence relation.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2014 (Online) 9th April)

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