JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q61

MathematicsSingle correct+4 / -1Question 61 of 90

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

reflexive and symmetric but not transitive.

reflexive and transitive but not symmetric.

symmetric and transitive but not reflexive.

an equivalence relation.

Answer and worked solution

Official answer: D

$\sec^2a=1+\tan^2a$ , so $(a,b)\in P\iff\tan^2a=\tan^2b$ (for $a$ , $b$ where tan is defined).

Equality of $\tan^2$ is reflexive, symmetric and transitive, so $P$ is an equivalence relation.

JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 61