Home
Class 12
MATHS
Evaluate |(cosalphacosbeta,cosalpha sinb...

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

Text Solution

Verified by Experts

Given `|(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha)|`
If we follow row wise operation we get
`[R_1=R_1-(cotalpha)R_3]`
`=|[0 , 0 , -cosecalpha],[-sinbeta, cosbeta , 0],[sinalphacosbeta , sinalphasinbeta ,cosalpha]|`
...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.7|17 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos

Similar Questions

Explore conceptually related problems

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

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

Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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

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

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

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

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

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)

If cosalpha+cosbeta=a ,sinalpha+sinbeta=b and alpha-beta=2theta, then (cos3theta)/(costheta)=

NCERT ENGLISH-DETERMINANTS-All Questions
  1. Solve system of linear equations, using matrix method, 5x + 2y = 3" "...

    Text Solution

    |

  2. Without expanding the determinant, prove that |(a,a^2,bc),(b,b^2,ca),(...

    Text Solution

    |

  3. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

    Text Solution

    |

  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

    Text Solution

    |

  5. Solve the equation |(x+a, x,x),(x,x+a, x),(x,x,x+a)|=0, a!= 0

    Text Solution

    |

  6. Prove: |a^2b c a c+c^2a^2+a bb^2a c a bb^2+b cc^2|=4a^2b^2c^2

    Text Solution

    |

  7. Solve system of linear equations, using matrix method, 2x+y+z=1" "x-2...

    Text Solution

    |

  8. Solve system of linear equations, using matrix method, x - y + z = 4"...

    Text Solution

    |

  9. The sum of three numbers is 6. If multiply theird number by 3 and add ...

    Text Solution

    |

  10. Solve the following system of equations by matrix method. 3x-2y + 3z=...

    Text Solution

    |

  11. Solve the system of equations2x + 5y = 1 and 3x + 2y = 7

    Text Solution

    |

  12. Show that the matrix A=[2 3 1 2]satisfies the equation A^2-4A+I=0

    Text Solution

    |

  13. If A=[[2,3],[1,-4]]and B=[[1,-2],[-1,3]], then verify that (A B)^(-1)=...

    Text Solution

    |

  14. If A=[[1 ,3 ,3],[ 1, 4 ,3],[ 1, 3, 4]],then verify thatA a d j A = |A|...

    Text Solution

    |

  15. Find adj for A=[[2 , 3 ] , [1 , 4]]

    Text Solution

    |

  16. Find minors and cofactors of the elements of the determinant|2-3 5 6 ...

    Text Solution

    |

  17. Find minors and cofactors of the elements a(11), a(21)in the determin...

    Text Solution

    |

  18. Find minors and cofactors of all the elements of the determinant |[1,...

    Text Solution

    |

  19. Using the property of determinants and without expanding, prove that:...

    Text Solution

    |

  20. Using the property of determinants and without expanding, prove that:...

    Text Solution

    |