Home
Class 12
MATHS
If x+(1)/(x)=2cos alpha then x^(n)+(1)/(...

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

A

`2^(n) cos alpha`

B

`2^(n) cos n alpha`

C

`2 i sin n alpha`

D

`2 cos n alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMMON ENTRANCE TEST -2016

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos
  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

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 :

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. Which of the following is a fourth root of

    Text Solution

    |

  2. If omega=(-1+i sqrt(3))/(2) then (3+omega+3 omega^(2))^(4)=

    Text Solution

    |

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

    Text Solution

    |

  4. The smallest positive integer for which(1 + i)^(2n)=(1 -l)^(2n) is

    Text Solution

    |

  5. The real part of (1)/(1+cos theta+i sin theta) is

    Text Solution

    |

  6. The modulus and amplitude of (1+2i)/(1-(1-i)^(2)) are respectively

    Text Solution

    |

  7. The complex number ((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(...

    Text Solution

    |

  8. If 2x=-1+sqrt(3)i, then the value of (1-x^(2)+x)^(6)-(1-x+x^(2))^(6)=

    Text Solution

    |

  9. The modulus of amplitude of (1+i sqrt(3))^(8) are respectively

    Text Solution

    |

  10. The conjugate of (3-2 i)/(5+7 i) is

    Text Solution

    |

  11. If x^(2)-x+1=0 then the value of sum(n=1)^(5)(x^(n)+(1)/(x^(n)))^(2) ...

    Text Solution

    |

  12. The conjugate of the complex number (1 + i)^(2)/(1-i) is

    Text Solution

    |

  13. The real and imaginary part of log (e)(1+sqrt(3) i) are

    Text Solution

    |

  14. The amplitude of "sin"(pi)/(5)+i(1-"cos"(pi)/(5)) is

    Text Solution

    |

  15. Let z and w be two non-zero complex numbers such that |z|=|w| and arg....

    Text Solution

    |

  16. The locus of the centre of a circle which touches the circles |z-z(1)|...

    Text Solution

    |

  17. Let z(1) and z(2) be two roots of the equation z^(2)+az+b=0, z being c...

    Text Solution

    |

  18. If z and w are two non-zero complex numbers such that |zw|=1 and arg(z...

    Text Solution

    |

  19. If ((1+i)/(1-i))^(x)=1, then x=

    Text Solution

    |

  20. If 1, omega, omega^(2) are the cube roots of unity, then [[1, omega^...

    Text Solution

    |