Home
Class 12
MATHS
Ecaluate [{:(cosalphacosbeta,cosalphas...

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

Text Solution

Verified by Experts

The correct Answer is:
`1`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Check your understanding|10 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Competition file|14 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise|4 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

Prove that |[cos alpha cos beta, cos alpha sin beta , sin alpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta, sinalpha sinbeta, cos alpha]|=cos2alpha

If cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?

(1+cosalphacosbeta)^2-(cosalpha+cosbeta)^2=

Evaluate : Delta=|{:(0,sinalpha,-cosalpha),(-sinalpha,0,sinbeta),(cosalpha,-sinbeta,0):}| .

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

Show by vector method that sin(alpha-beta)=sinalphacosbeta-cosalpha sinbeta.

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

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

If neither alpha nor beta is a multiple of pi/2 and the product AB of matrices A=[(cos^2alpha, cosalpha sin alpha),(cosalpha sinalpha, sin^2alpha)] and B=[(cos^2beta, cosbeta sinbeta),(cosbetasinbeta, sin^2beta)] is a null matrix then alpha- beta is (A) 0 (B) an odd mutiple of pi/2 (C) a multiple of pi (D) none of these

MODERN PUBLICATION-DETERMINANTS-Revision Exercise
  1. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

    Text Solution

    |

  2. Prove that Delta=[a+b x c+dx p+q x a x+b c x+d p x+q u v w]=(1-x^2)|a ...

    Text Solution

    |

  3. Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,co...

    Text Solution

    |

  4. If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+...

    Text Solution

    |

  5. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  6. If a,b,c are in A.P. find the value of: ||2y+4, 5y+7, 8y+a],[3y+5, 6y+...

    Text Solution

    |

  7. If ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+n)(l'x+m'y+n'), then prove tha...

    Text Solution

    |

  8. If a+b+c=0 and |[a-x,c,b],[c,b-x,a],[b,a,c-x]|=0 then x=

    Text Solution

    |

  9. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

    Text Solution

    |

  10. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

    Text Solution

    |

  11. If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

    Text Solution

    |

  12. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}], then show that A^(3)=A^(-1).

    Text Solution

    |

  13. If A=[1tanx-tanx1] , show that A^T\ A^(-1)=[cos2x-sin2xsin2xcos2x] .

    Text Solution

    |

  14. If A=[(2,-3),(4,6)] " verify that " (adj A)^(-1)=(adj A^(-1)).

    Text Solution

    |

  15. Prove that : adj. I(n)=I(n)

    Text Solution

    |

  16. Prove that : adj.O=O

    Text Solution

    |

  17. Prove that : I(n)^(-1)=I(n)

    Text Solution

    |

  18. Find the inverse of each of the matrices given below : Let D= "dia...

    Text Solution

    |

  19. Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}...

    Text Solution

    |

  20. Find the inverse of each of the matrices given below : Obtain the in...

    Text Solution

    |