Prove that: `sin (n + 1) x sin (n + 2)x + cos (n + 1) x cos (n + 2) x = cos x`

Prove the following: sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos 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)

Prove that nC_ (1) sin x * cos (n-1) x + nC_ (2) sin2x * cos (n-2) x + nC_ (3) sin3x * cos (n-3) x + ... + nC_ ( n) sin nx = 2 ^ (n-1) sin nn

Prove that sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

Prove that sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

Prove that: sin(n+1)A sin(n+2)A+cos(n+1)A cos(n+2)A=cos A

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

sin x = 2 ^ (n) * cos (x) / (2) * cos (x) / (2 ^ (2)) * cos (x) / (2 ^ (3)) * ... * cos ( x) / (2 ^ (n)) * sin (x) / (2 ^ (n))