Q77.Let P be the relation defined on the set of all real numbers such that P = {(a, b) : sec2 a −tan2 b = 1}. Then, P is (1) reflexive and symmetric but not transitive (2) symmetric and transitive but not reflexive (3) reflexive and transitive but not symmetric (4) an equivalence relation
What This Question Tests
The question requires determining if a given relation is reflexive, symmetric, or transitive. The key insight is to simplify the given condition sec²a - tan²b = 1 using trigonometric identities to tan²a = tan²b, which makes checking the properties straightforward.
Concepts Tested
Formulas Used
sec²θ - tan²θ = 1
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📋 Question Details
- Chapter
- Sets Relations Functions
- Topic
- Types of relations
- Year
- 2014
- Shift
- 09 Apr Online
- Q Number
- Q77
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 1: Relations and Functions
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