wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

For any two real number θ and ϕ where, θ,ϕ(π2,π2). We define θRϕ if and only if sec2θtan2ϕ=1. Then relation R is

A
Reflexive but not transitive relation.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Symmetric but not reflexive relation.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Both reflexive and symmetric relation but not transitive relation.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
An equivalence relation
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D An equivalence relation
sec2θtan2θ=1 θ(π2,π2) So, R is a reflexive relation

Let (θ,ϕ)Rsec2θtan2ϕ=1
1+tan2θ(sec2ϕ1)=1
sec2ϕtan2θ=1
(ϕ,θ)R
So, R is a symmetric relation.

Let (θ,ϕ)Rsec2θtan2ϕ=1 (1)
and (ϕ,α)Rsec2ϕtan2α=1 (2)
From (1) and (2)
sec2θtan2α=1
(θ,α)R
So, R is a transitive relation.
Hence, R is an equivalence relation

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Sets and Their Representations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon