If `alpha,beta!=0` , and `f(n)""=alpha^n+beta^n` and `|3 1+f(1)1+f(2)1+f(1)1+f(2)1+f(3)1+f(2)1+f(3)1+f(4)|=K(1-alpha)^2(1-beta)^2(alpha-beta)^2` , then K is equal to (1) `alphabeta` (2) `1/(alphabeta)` (3) 1 (4) `-1`

If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and {:|(3, 1+f(1),1+f(2)), (1+f(1),1+f(2),1+f(3)), (1+f(2),1+f(3),1+f(4))|:}=K(1-alpha)^2(1-beta)^2(alpha-beta)^2 , then K is equal to (1) alphabeta (2) 1/(alphabeta) (3) 1 (4) -1

f(1)=1, n ge 1 f(n+1)=2f(n)+1 then f(n)=

If cos(alpha-beta)=3sin(alpha+beta),t h e n 1/(1-3sin2alpha)+1/(1-3sin2beta)= (a) 1/2 (b) (-1)/2 (c) 1/4 (d) (-1)/4

If cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2beta)= 1/2 (b) (-1)/2 (c) 1/4 (d) (-1)/4

Let f(theta)=cottheta/(1+cottheta) and alpha+beta=(5pi)/4 then the value f(alpha)f (beta) is

If f(x)=(cotx)/(1+cotx)andalpha+beta=(5pi)/(4) , then find f(alpha).f(beta) .

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If alpha and beta are the zeros of the quadratic polynomial f(x)=a x^2+b x+c , then evaluate: (i) alpha^2beta+alphabeta^2 (ii) alpha^4+beta^4 (iii) 1/(aalpha+b)+1/(abeta+b)

Let f(n)=2cosn xAAn in N , then f(1)f(n+1)-f(n) is equal to f(n+3) (b) f(n+2) f(n+1)f(2) (d) f(n+2)f(2)

If alpha, beta be the roots of ax^(2)+bx+c=0(a, b, c in R), (c )/(a)lt 1 and b^(2)-4ac lt 0, f(n)= sum_(r=1)^(n)|alpha|^(r )+|beta|^(r ) , then lim_(n to oo)f(n) is equal to