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

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

Prove that (i) " cos " ((pi)/(4) + x) + " cos " ((pi)/(4)- x) =sqrt(2) " cos " x (ii) " cos " ((3pi)/(4) + x) - "cos " ((3pi)/(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

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

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

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

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

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

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

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)