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Jee Main 2025 — Medium JEE math MCQ

Define a relation \( R \) on the interval \( [0, \frac{\pi}{4}] \) by \( xRy \) if and only if \( \sec^2 x - \tan^2 y = 1. \) Then \( R \) is
  1. A. both reflexive and transitive but not symmetric
  2. B. an equivalence relation
  3. C. reflexive but neither symmetric nor transitive
  4. D. both reflexive and symmetric but not transitive

Solution

The correct option is **B**. (B. an equivalence relation)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Define a relation R R on the interval [0,π4] [0, \frac{\pi}{4}] by xRy xRy if and only if sec⁡2x−tan⁡2y=1. \sec^2 x - \tan^2 y = 1. Then R R is
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep