evaluate `cos((3 pi)/(4)+x)-sin((pi)/(4)-x)`

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

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

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

Evaluate :cos^(2)((pi)/(4)+x)-sin^(2)((pi)/(4)-x)

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

Prove the following 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

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

Prove that (i) cos (n + 2) x cos (n+1) x +sin (n+2) x sin (n+1) x = cos x) (ii) " cos " .((pi)/(4)-x) " cos " .((pi)/(4)-y) " - sin " ((pi)/(4)-x ) " sin " ((pi)/(4) -y) =" sin " (x+y)

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 .