Home
Class 11
MATHS
If x1, x2, x3, x4 are roots of the equat...

If `x_1, x_2, x_3, x_4` are roots of the equation `x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0`, then `sum_(i=1)^4tan^-1x_i` is equal to

A

`beta`

B

`pi/2-beta`

C

`pi-beta`

D

`-beta`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|21 Videos

  • TRIGONOMETRIC FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

If x_1, x_2, x_3 and x_4 are the roots of the equations x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0, prove that tan^(-1)x_1+tan^(-1)x_2+tan^(-1)x_3+tan^(-1)x_4=(pi/2)-beta .

IF the roots of the equation 3x^2+8x+2=0 are alpha,beta then (1/alpha+1/beta) =

Solve the equation sin^4x+cos^4x-2sin^2x+(3sin^2 2x)/4=0

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

Determine the sum of imaginary roots of the equation (2x^2+x-1) (4x^2+2x-3)=6

If cos^4theta+alpha and sin^4theta+alpha are the roots of the equation x^2+2b x+b=0 and cos^2theta+beta,sin^2theta+beta are the roots of the equation x^2+4x+2=0, then values of b are a) 2 b) -1 c) -2 d) 1

If tan(alpha/2) and tan(beta/2) are the roots of the equation 8x^2-26x+15=0 then cos(alpha+beta) is equal to

The roots of 2(1+i)x^2-4(2-i)x-5-3i=0 are-

Roots of the equation 3x^2 -6x+4=0 are alpha and beta then find the value of alpha^3 +beta^3

PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. The number of solution of the equation 2tanx+x=(12pi)/5 in the interva...

    Text Solution

    |

  2. The value of cos^-1(cos5) is

    Text Solution

    |

  3. If x1, x2, x3, x4 are roots of the equation x^4-x^3sin2beta+x^2cos2bet...

    Text Solution

    |

  4. If x+1/x=2, the principle value ot sin^-1x is

    Text Solution

    |

  5. If cos^-1x+cos^-1y+cos^-1z=3pi, then xy+yz+zx is equal to

    Text Solution

    |

  6. If 1-tanx/1+tanx=tany and x-y=pi/6, then x, y are respectively

    Text Solution

    |

  7. If cos^4x+4sin^4x=1, then general value of x equals to

    Text Solution

    |

  8. The equation sinx=[1+sinx]+[1-cosx] has [where [.] is greatest integer...

    Text Solution

    |

  9. The equation 8x^3-6x+sqrt3=0 is satisfied by

    Text Solution

    |

  10. Number of values of theta which satisfy sin^2theta-2sin^2theta-1=0 is

    Text Solution

    |

  11. Which of the following is true?

    Text Solution

    |

  12. theta=tan^-1(2tan^2theta)-tan^-1{(1/3)tantheta}, if

    Text Solution

    |

  13. sec(cosec^-1x) is equal to

    Text Solution

    |

  14. The solution of the equation sin[2cos^-1{cot(2tan^-1x)}] = 0 are

    Text Solution

    |

  15. Let f(x)=e^(cos^-1sin(x+pi/3)), then

    Text Solution

    |

  16. The greatest and least values of (sin^-1x)^3+(cos^-1x)^3 are

    Text Solution

    |

  17. alpha is a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a...

    Text Solution

    |

  18. alpha is a root of the equation (2sinx-cosx)(1+cosx)=sin^2x beta is a...

    Text Solution

    |

  19. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

    Text Solution

    |

  20. f(x)=sin{cot^-1(x+1)}-cos(tan^-1x) a=costan^-1sincot^-1x b=cos(2cos^-1...

    Text Solution

    |