The path difference between the two waves y1=a1sin⁡ωt-2πxλ and y2=a2cos⁡ωt-2πxλ+ϕ is

y1=a1sin⁡ωt−2πxλy2=a2sin⁡ωt−2πxλ+ϕ+π2Phase difference                       =ωt−2πxλ+ϕ+π2−ωt−2πxλ=ϕ+π2 Path difference =λ2π× Phase difference =λ2πϕ+π2