L.H.S. = cos (

π

4

−x) cos (

π

4

−y) - sin (

π

4

−x) sin (

π

4

−y)
= cos (

π

4

−x+

π

4

−y) [Since cos (A + B) = cosA cosB – sinA sinB]
= cos (

π

2

−(x+y)) = sin (x + y) = R.H.S. (Since cos (π/2 - θ) = sin θ)