Pls give the solution of this question using circular motion

Solution:

Let equation of motion to particles be given by,
x₁​=Asin(ωt) 
and x₂​=Asin(ωt+ϕ)
Representing it as a phasor diagram:



So initial phase difference between two particles is ϕ.
Now, 
x₂​−x₁​=A[sin(ωt+ϕ)−sin(ωt)]
         =2asin(2ωt+ϕ−ωt​)cos(2ωt+ϕ+ωt​)
​​​​​​         =2asin(ϕ/2)cos(ωt+ϕ/2)
Maximum value of above expression is 2asin(ϕ/2)=2​a
⟹sin(ϕ/2)=1/2​
⟹ϕ/2=π/4
⟹ϕ = π/2=90 degree