" (v) "sin((pi)/(4)+x)-sin((pi)/(4)-x)=sqrt(2)sin x

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

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

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

Prove that cos ((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt2 sin x

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