`sin(pi/4+A).sin(pi/4-A)=1/2 cos2A`

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

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

Let Q = [{: (cos ""(pi)/(4) , - sin""(pi)/(4)),(sin""(pi)/(4), cos""(pi)/(4)):}] and x = [{:((2)/(sqrt(2))),((1)/(sqrt(2))):}] then Q^(3) x is equal to

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

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

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

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

prove that sin((pi)/(4)+x)+sin((pi)/(4)-x)=sqrt(2)cos x