JEE Mains · Maths · STD 12 - 1. relation and function
Define a relation R on the interval \(\left[0, \frac{\pi}{2}\right)\) by \(x \mathrm{R} y\) if and only if \(\sec ^2 x-\tan ^2 y=1\). Then R is :
- A both reflexive and transitive but not symmetric
- B an equivalence relation
- C reflexive but neither symmetric not transitive
- D both reflexive and symmetric but not transitive
Answer & Solution
Correct Answer
(B) an equivalence relation
Step-by-step Solution
Detailed explanation
\begin{aligned} & \sec ^2 x-\tan ^2 x=1 \quad(\text { on replacing } y \text { with } x) \\ & \Rightarrow \text { Reflexive } \\ & \sec ^2 x-\tan ^2 y=1 \\ & \Rightarrow 1+\tan ^2 x+1-\sec ^2 y=1 \\ & \Rightarrow \sec ^2 y-\tan ^2 x=1 \\ & \Rightarrow \text { symmetric } \\ &…
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