Home
Class 12
MATHS
Without expanding evaluate the determ...

Without expanding evaluate the determinant `|sinalphacosalphasin(alpha+delta)sinbetacosbetasin(beta+delta)singammacosgammasin(gamma+delta)|` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

Prove that |(sin alpha,cos alpha,sin(alpha+delta)),(sin beta,cos beta,sin(beta+delta)),(sin gamma,cos gamma,sin(gamma+delta))|=0

Without expanding, show that the value of each of the determinants is zero: |sinalphacosalpha"cos"(alpha+delta)sinbetacosbeta"cos"(beta+delta)singammacosgamma"cos"(gamma+delta)|

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0

Using properties of determinants. Prove that |(sinalpha,cosalpha,cos(alpha+delta)),(sinbeta,cosbeta,cos(beta+delta)),(singamma,cosgamma,cos(gamma+delta))|=0

Without expanding, show that the value of the following determinant is zero: |[sinalpha,cosalpha,cos(a+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]|

Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+alpha),cos(x+alpha),a+xsinalpha),(sin(x+beta),cos(x+beta),b+xsinbeta),(sin(x+gamma),cos(x+gamma),c+xsingamma):}| is independent of x .

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

Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)| .

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Find the value of the determinant =|(2, 3, 4) ,(5, 6, 8),( 6x,9x, 12...

    Text Solution

    |

  2. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

    Text Solution

    |

  3. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

    Text Solution

    |

  4. Without expanding evaluate the determinant |(a^x+a^-x)^2(a^x-a^-x)^2 1...

    Text Solution

    |

  5. If a ,\ b ,\ c are in A.P., find the value of |(2y+4, 5y+7, 8y+a),(3...

    Text Solution

    |

  6. Without expanding evaluate the determinant =|(265, 240, 219), (240, ...

    Text Solution

    |

  7. If D1=|1 1 1 x^2 y^2 z^2 x y z| and D2=|1 1 1y z z xx y x y z| , with...

    Text Solution

    |

  8. Let D=|Ax x^2 1 By y^2 1 Cz z^2 1| and D1=|A B C x y z yz zx xy| ...

    Text Solution

    |

  9. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

    Text Solution

    |

  10. If A is a skew-symmetric matrix of odd order n , then |A|=O .

    Text Solution

    |

  11. Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

    Text Solution

    |

  12. Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b)...

    Text Solution

    |

  13. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

    Text Solution

    |

  14. Prove that: |-a^2 ab ac ba -b^2 bc ...

    Text Solution

    |

  15. Prove that: |(1, 1, 1),( 1, 1+x,1) ,(1, 1, 1+y)|=x y .

    Text Solution

    |

  16. Evaluate: |(1,a ,a^2), (1,b,b^2) ,(1,c,c^2)| .

    Text Solution

    |

  17. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

    Text Solution

    |

  18. Prove that: |[alpha,beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,g...

    Text Solution

    |

  19. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

    Text Solution

    |

  20. In a A B C ,if|1 1 1 1+cosA 1+cosB 1+cosC cos^2A+A cos^2B+cosB cos^2...

    Text Solution

    |