The value of cos⁡ycos⁡π2−x−cos⁡π2−ycos⁡x+sin⁡ycos⁡π2−x+cos⁡xsin⁡π2−y is zero if

The given expression iscosy sinx - siny cosx + sin y sinx+ cos x cos y sin(x - y) + cos(x -y) = 0⇒ 212sin⁡(x−y)+12cos⁡(x−y)=0 or  sin⁡x−y+π4=0⇒ π4+x−y=nπ,n∈Z⇒ x−y=nπ−π4,n∈Z⇒ x=nπ−π4+y, where n∈Z