Prove the following `cos(pi/4-x)cos(pi/4-y)-sin(pi/4-x)sin(pi/4-y)=sin(x+y)`

cos(pi/4-A)cos(pi/4-B)-sin(pi/4-A)sin(pi/4-B)=sin(A+B)

cos(pi/4-A)-sin(pi/4+A)=0

Prove that: cos((pi)/(4)-x)cos((pi)/(4)-y)-sin((pi)/(4)-x)sin((pi)/(4)-y)=sin(x+y)

cos((3pi)/4+x)-sin(pi/4-x)=?

Prove that: cos((pi)/(4)-A)cos((pi)/(4)-B)-sin((pi)/(4)-A)sin((pi)/(4)-B)=sin(A+B)

Evaluate the following: (cos(2 pi))/(3)(cos pi)/(4)-(sin(2 pi))/(3)(sin pi)/(4)

sin (pi/2) = 2 sin(pi/4) cos (pi/4)

Prove the following: (i) cos((3pi)/(4)+x)-cos((3pi)/(4)-x)=-sqrt2 sin x (ii) cos"((pi)/(4)+x)+cos((pi)/(4)-x)=sqrt2 cos x .

Prove that cos((pi)/(4)-x)cos((pi)/(4)+x)=(1)/(2)-sin^(2)x

Prove that: cos((3 pi)/(4)+x)-cos((3 pi)/(4)-x)=-sqrt(2)sin x