The correct option is D An equivalence relation
∵sec2θ−tan2θ=1 ∀ θ∈(−π2,π2) So, R is a reflexive relation
Let (θ,ϕ)∈R⇒sec2θ−tan2ϕ=1
⇒1+tan2θ−(sec2ϕ−1)=1
⇒sec2ϕ−tan2θ=1
⇒(ϕ,θ)∈R
So, R is a symmetric relation.
Let (θ,ϕ)∈R⇒sec2θ−tan2ϕ=1 …(1)
and (ϕ,α)∈R⇒sec2ϕ−tan2α=1 …(2)
From (1) and (2)
⇒sec2θ−tan2α=1
⇒(θ,α)∈R
So, R is a transitive relation.
Hence, R is an equivalence relation