Home
Class 11
MATHS
Find the value of x such that ((x+alpha)...

Find the value of `x` such that `((x+alpha)^n-(x+beta)^n)/(alpha-beta)=(sin (ntheta))/(sin^n theta)`, where `alpha` and `beta` are the roots of the equation `t^2-2t+2=0`.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

Find the value of (sin (alpha + beta))/(sin (alpha - beta)), "given that" tan alpha = 2 tan beta.

Prove that , tan(alpha+beta)tan(alpha-beta)=(sin^2alpha-sin^2beta)/(cos^2alpha-sin^2beta)

If tan ( alpha-beta) = (sin 2 beta)/(5-cos 2 beta),"find the value of " tan alpha : tan beta.

IF alpha and beta are the roots of the equation x(x-3)=4, find the value of alpha^2+beta^2 .

Show that sin^2(x+alpha)+sin^2(x+beta)-2cos(alpha-beta).sin(x+alpha)sin(x+beta) is independatn of x.

If sec(alpha-beta)=sqrt(2) and sin(alpha+beta)=(1)/(2) , then find the least positive values of alpha and beta .

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

The value of ((cos alpha + cos beta)/(sin alpha - sin beta))^(n) + ((sin alpha + sin beta)/(cos alpha - cos beta))^(n) (where n is a whole number ) is equal to-

If sin ( alpha + beta ) =(4)/(5) and sin (alpha - beta ) =(5)/(13), find the value of tan 2 alpha

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Given that x^2-3x+1=0, then the value of the expression y=x^9+x^7+x^(-...

    Text Solution

    |

  2. If i z^4+1=0, then prove that z can take the value cospi//8+isinpi//...

    Text Solution

    |

  3. Find the value of x such that ((x+alpha)^n-(x+beta)^n)/(alpha-beta)=(s...

    Text Solution

    |

  4. Suppose a ,b ,c in I such that the greatest common divisor for x^2+a ...

    Text Solution

    |

  5. Find the value of following expression: [(1-cospi/(10)+isinpi/(10))/(1...

    Text Solution

    |

  6. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

    Text Solution

    |

  7. If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consec...

    Text Solution

    |

  8. If z1, z2 in C ,z1^2+z2^2 in R ,z1(z1^2-3z2^2)=2 and z2(3z1^2-z2^2)...

    Text Solution

    |

  9. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

    Text Solution

    |

  10. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then find the valu...

    Text Solution

    |

  11. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

    Text Solution

    |

  12. The set {R e((2i z)/(1-z^2)): z is a complex number , |z|=1,z=+-1} is...

    Text Solution

    |

  13. If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, the...

    Text Solution

    |

  14. If a r g["z"1("z"3-"z"2)]=a r g["z"3("z"2-"z"1)] , then prove that O ,...

    Text Solution

    |

  15. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

    Text Solution

    |

  16. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

    Text Solution

    |

  17. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  18. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

    Text Solution

    |

  19. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

    Text Solution

    |

  20. Find the real values of x and y for which the following equation is sa...

    Text Solution

    |