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

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

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

sin^(m)x.cos^(n)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)

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