`sin (n+1) x sin (n+2) x + cos (n+1)x cos (n+2)x=cos x`

sin (n + 1) A sin (n-1) A + cos (n + 1) A cos (n-1) A = cos2A

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) A * sin (n-1) A + cos (n + 1) A * cos (n-1) A = cos2A

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

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)

Solve for x the equation |(a^(2),a,1),(sin(n+1)x,sin nx,sin(n-1)x),(cos(n+1)x,cosn x,cos(n-1)x)|=0

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

The value of the determinant |a^(2)a1cos nx cos(n+1)x cos(n+2)x sin nx sin(n+1)x sin(n+2)x is independent of n(b)a(c)x(d) none of these