Prove that : `(cos x + cos y)^2 + (sin x - sin y)^2 = 4 cos^2\ (x+y)/2`

Prove that: quad (cos x+cos y)^(2)+(sin x-sin y)^(2)=4cos^(2)(x+y)/(2)

Prove that cos (x + y) = cos x cos y-sin x sin y

Prove that: quad (cos x-cos y)^(2)+(sin x-sin y)^(2)=4sin^(2)(x-y)/(2)

prove that: cos ^ (2) x + cos ^ (2) y-2cos x * cos y * cos (x + y) = sin ^ (2) (x + y)

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

If (cos ^ (4) x) / (cos ^ (2) y) + (sin ^ (4) x) / (sin ^ (2) y) = 1 then prove that (cos ^ (4) y) / (cos ^ (2) x) + (sin ^ (4) y) / (sin ^ (2) x) = 1

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)

If cos x + cos y =2, then value of sin x + sin y is

cos x + cos y + cos z = 0 and sin x + sin y + sin, then cos ^ (2) ((xy) / (2)) =

lf_ (cos x + cos y-cos z = 0 = sin x + sin y + sin) then cos ((xy) / (2)) =