Home
Class 12
MATHS
If A(theta)=[(1, than theta),(-tan, thet...

If `A(theta)=[(1, than theta),(-tan, theta=1)]` and `AB=l`, then `(sec^(2)theta)B` is equal to

A

`A(theta)`

B

`A((theta)/2)`

C

`A(-theta)`

D

`A(-(theta)/2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `AB=l`
`impliesB=A^(-1)impliesB=1/(|A|)adj(A)`
`=1/(1+tan^(2)theta)[(1,-tan theta),(tan theta,1)]`
`B=1/(sec^(2)theta)[(1,-tan theta),(tan theta,1)]`
`implies(sec^(2) theta)B=[(1,-tan theta),(tan theta,1)]=A(-theta)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATHEMATICAL LOGIC

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|22 Videos

  • MHTCET 2007

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

If tan^2 theta =(1-e^2) , then sec theta+tan^3 theta "cosec" theta is equal to

tan theta+(1)/(tan theta)=sec theta cosec theta

(sin theta tan theta)/(1-cos theta)=1+sec theta

cos theta(tan theta+2)(2tan theta+1)=2sec theta+5sin theta

cos theta(tan theta+2)(2tan theta+1)=2sec theta+5sin theta

cos theta(tan theta+2)(2tan theta+1)=2sec theta+5sin theta

For 0 prec theta prec 90 , if (sec theta( 1- sin theta)(sec theta+tan theta))/(sec theta-tan theta)^2=(1+k)/(1-k) , then k is is equal to : 0 prec theta prec 90 के लिए , यदि (sec theta( 1- sin theta)(sec theta+tan theta))/(sec theta-tan theta)^2=(1+k)/(1-k) है, तो k का मान किसके बराबर है ?

(tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta*cos ec theta

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATRICES-MISCELLANEOUS PROBLEMS
  1. Let {:A=[(1,2),(-5,1)]and A^(-1)=xA+yI:}, then the values of x and y a...

    Text Solution

    |

  2. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

    Text Solution

    |

  3. If A(theta)=[(1, than theta),(-tan, theta=1)] and AB=l, then (sec^(2)t...

    Text Solution

    |

  4. If A=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha,0),(0,0,1)] the...

    Text Solution

    |

  5. Suppose A is a matrix of order 3 and B=|A|A^(-1). If |A|=5, then |B| i...

    Text Solution

    |

  6. if[{:(2,1),(3,2):}]A[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}],"then" A=?

    Text Solution

    |

  7. If f(theta)=[(cos theta, -sin theta,0),(sin theta, cos theta, 0),(0,0,...

    Text Solution

    |

  8. If A is a singular matrix, then Aadj(A) is a/an

    Text Solution

    |

  9. If k is a scalar and l is a unit matrix of order 3 then adj(kl) is equ...

    Text Solution

    |

  10. Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambda...

    Text Solution

    |

  11. Let a, b, c be any real numbers. Suppose that there are real numbers...

    Text Solution

    |

  12. Let a, b, c be positive real numbers. The following system of equation...

    Text Solution

    |

  13. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |

  14. The symmetric part of the matrix A=[(1,2,4),(6,8,2),(2,-2,7)] is equal...

    Text Solution

    |

  15. If {:A=[(1,0,0),(0,1,0),(a,b,-1)]:}, then A^2 is equal to

    Text Solution

    |

  16. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

    Text Solution

    |

  17. If A is a 3xx3 such that |5.adj(A)|=5 then |A| is equal to

    Text Solution

    |

  18. If A=[(alpha, 2),(2, alpha)] and |A^(3)|=27 then alpha is equal to

    Text Solution

    |

  19. The elements in the first row and third column of the inverse of the m...

    Text Solution

    |

  20. If A=[(-1,3),(2,1)] then 1+A+A^(2)+…………..+oo is equal to

    Text Solution

    |