Home
Class 11
MATHS
The determinant D=|{:(cos(alpha+beta),-s...

The determinant `D=|{:(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sinalpha,cosalpha,sinbeta),(-cosalpha,sinalpha,cosbeta):}|` is independent of :-

A

`alpha`

B

`beta`

C

`alpha and beta`

D

neither `alpha " nor " beta`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|6 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

The value of the determinant Delta = |(cos (alpha + beta),- sin (alpha + beta),cos 2 beta),(sin alpha,cos alpha,sin beta),(- cos alpha,sin alpha,- cos beta)| , is

sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}]

If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta) =

Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,cosbeta,0),(sinalphacosbeta,sinalpha sinbeta,cosalpha)|

Evaluate: =|[0,sinalpha,-cosalpha],[-sinalpha,0,sinbeta],[cosalpha,-sinbeta,0]|

If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be (a) -sinalpha (b) sinbeta (c) cosalpha (d) cosbeta

Evaluate |{:(cos alpha cos beta,,cos alphasinbeta,,-sinalpha),(-sinbeta,,cos beta,,0),(sinalpha cos beta,,sinalphasinbeta,,cos alpha):}|

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

    Text Solution

    |

  2. If the system of equations x + ay + az = 0 bx + y + bz = 0 cx + ...

    Text Solution

    |

  3. The determinant D=|{:(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sina...

    Text Solution

    |

  4. If omega is a cube root of unity, then Root of polynomial is |(x + 1...

    Text Solution

    |

  5. " If " Delta(1) =|{:(x,,b,,b),(a,,x,,b),(a,,a,,x):}|" and " Delta(2)...

    Text Solution

    |

  6. If y= sin px and y(n) is the nth derivative of y, then |{:(y,y(1),y(...

    Text Solution

    |

  7. If |p b c a q c a b r|=0 , find the value of p/(p-a)+q/(q-b)+r/(r-c),\...

    Text Solution

    |

  8. Using properties of determinants, show that |{:(x, p, q), ( p, x, q)...

    Text Solution

    |

  9. The factors of |(x,a,b),(a,x,b),(a,b,x)|, are

    Text Solution

    |

  10. Let omega=-1/2+i(sqrt(3))/2dot Then the value of the determinant |1 1 ...

    Text Solution

    |

  11. If a+b+c=0, one root of |a-x c b c b-x a b a c-x|=0 is x=1 b. x=2 c. ...

    Text Solution

    |

  12. suppose D= |{:(a(1),,b(1),,c(1)),(a(2),,b(2),,c(2)),(a(3),,b(3),,c(3...

    Text Solution

    |

  13. A and B are two non-zero square matrices such that AB = O. Then,

    Text Solution

    |

  14. The roots of the equation |{:(x-1,1,1),(1,x-1,1),(1,1,x-1):}|=0 are

    Text Solution

    |

  15. From the matrix equation AB=AC, we conclude B=C provided.

    Text Solution

    |

  16. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

    Text Solution

    |

  17. The value of |(11,12,13),(12,13,14),(13,14,15)|, is

    Text Solution

    |

  18. |{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is equal to:

    Text Solution

    |

  19. If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|, then

    Text Solution

    |

  20. Let a ,b , c be the real numbers. The following system of equations in...

    Text Solution

    |