If x+(1)/(x)=2cos alpha then x^(n)+(1)/(...

If `x+(1)/(x)=2cos alpha` then `x^(n)+(1)/(x^(n))`=

A

`2i"sin"nalpha`

B

`2"cos"nalpha`

C

`2^n"cos"alpha`

D

`2^n"cos"nalpha`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

The coefficient of (1)/(x) in the expansion of ((1)/(x)+1)^(n)(1+x)^(n) is

If x= npi+(-1)^(n)alpha , n in I and x=npi+(-1)^(n)beta are the roots of 4 cos x -3 sec x =tan x , then 4(sin alpha + sin beta ) is

If 1+x^(2)=sqrt(3)x , then sum_(n=1)^(24)(x^(n)-(1)/(x^(n)))^(2) equals

If cos^(-1) x - cos ^(-1) (y)/(2) =alpha then 4x^(2) -4xy cos alpha+ y^(3) is equzal to

If n(ne 1) in N and I_(n) = int e^(x)/x^(n) dx then I_(n)+ e^(x)/((n-1)x^(n-1))

If y = tan^(-1) ((1)/(1 + x + x^(2))) + tan^(-1) ((1) /(x^(2) + 2x + 3)) + tan^(-1) ((1)/(x^(2) + 5x + 7)) + ….n terms , then y(0) is

If x^(2)-x+1=0 then the value of sum_(n=1)^(5)(x^(n)+(1)/(x^(n)))^(2) is

sum_(r=1)^(n)(2r-1)=x then lim_(n to oo) [(1^(3))/(x^(2))+(2^(3))/(x^(2))+(3^(3))/(x^(2))+ .......+(n^(3))/(x^(2))] =

The term independent of x in the expansion of (1+x)^(n)(1-(1)/(x))^(n) is:

The sum of : (x+ 2)^(n-1) + ( x+2) ^(n-2) (x+1) + ( x+2)^(n-3) (x+1)^(2) + "......." + ( x+ 1)^(n-1) equals :