L.H.S=cos(π4−x)cos(π4−y)−sin(π4−x)sin(π4−y)
Using formula, cos(A+B)=cos Acos B−sin Asin B
Let A=π4−x and B=π4−y
∴cos[(π4−x)+(π4−y)]
=cos[π4−x+π4−y]
=cos[π2−(x+y)]=sin(x+y){∵cos(π2−θ)=sinθ}
So, LH.S =R.H.S
cos(π4−x)cos(π4−y)−sin(π4−x)sin(π4−y)=sin(x+y)
Hence proved.