As α,β,γ,δ is in A.P
Let the common difference is r
Then, β=α+r,γ=α+2r,δ=α+3r
α+β+γ+δ=4α+6r
A:3β+δ=3α+3r+α+3r=4α+6r⇒sin(3β+δ)=sin(4α+6r)=sin(α+β+γ+δ)
B:α+3γ=α+3α+6r=4α+6r⇒sin(α+3γ)=sin(4α+6r)=sin(α+β+γ+δ)
C:α+3δ=4α+9r,⇒sin(α+3δ)=sin(4α+9r)≠sin(α+β+γ+δ)
D:3β+γ=4α+5r⇒sin(3β+γ)=sin(4α+5r)≠sin(α+β+γ+δ)
Hence, options 'A' and 'B' are correct.