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

The determinant Delta=|(a^2,a,1),(cos(nx),cos (n + 1) x,cos(n+2) x),(sin(nx),sin (n +1)x,sin (n + 2) x)| is independent of

The value of the determinants |{:(1,a,a^(2)),(cos(n-1)x,cos nx , cos(n+1)x),(sin(n-1)x , sin nx , sin(n+1)x):}| is zero if

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

If maximum and minimum values of the determinant |{:(1+sin^2x,cos^2x,sin2x),(sin^2x,1+cos^2x,sin2x),(sin^2x,cos^2x,1+sin2x):}| are alpha and beta then show that (alpha^(2n)-beta^(2n)) is always an even integer for n in N .

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

D(cos^(-1)x+sin^(-1)x)^(n)=

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

Prove that cos x+cos3x+cos5x+cos(2n-1)x=(sin2nx)/(2)sin x