Evaluate cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x)sin(π/4 - y)

cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x)sin(π/4 - y)

Using formula:cosA.cosB-sinA.sinB=cos(A+B)

cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x)sin(π/4 - y)
=cos{(π/4 - x)+(π/4 - y)}
=cos{π/4 - x+π/4 - y}
=cos{π/2 - x - y}
=cos{π/2 -( x + y)}
=sin( x + y) Ans.

cos(π/4 - x) cos(π/4 - y) - sin(π/4 - x)sin(π/4 - y)
= cos [(π/4 - x) + (π/4 - y)]
= cos [π/2 - (x + y)]
= sin (x + y) ANSWER