Home
Class 12
MATHS
If A=[[sin theta , cos theta],[-cos thet...

If `A=[[sin theta , cos theta],[-cos theta , -sin theta]]` then `A^(2)=`

A

`[[cos 2 theta ,sin 2 theta ] , [-sin 2 theta , -cos 2 theta]]`

B

`[[-cos 2 theta ,sin 2 theta ] , [ sin 2 theta , -cos 2 theta]]`

C

`[[-cos 2 theta ,sin 2 theta ] , [ -sin 2 theta , cos 2 theta]]`

D

`[[-cos 2 theta ,0 ] , [ 0 , -cos 2 theta]]`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    HIMALAYA PUBLICATION|Exercise Question Bank|97 Videos
  • MAXIMA AND MINIMA

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|167 Videos

Similar Questions

Explore conceptually related problems

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is

|[4 sin ^2 theta, cos 2 theta],[ -cos 2 theta,cos ^2 theta]| =

If A= [[cos theta,sin theta],[-sin theta,cos theta]], then lim _(n rarr infty )A^(n)/n is (where theta in R )

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1

If A_(theta) = [(cos theta ,sin theta ),(-sin theta ,cos theta )] then A_(alpha)A_(beta) equals :

(3 cos theta+cos 3 theta)/(3 sin theta-sin 3 theta)=

(sin 2 theta)/(1-cos 2 theta)=cot theta

(sin theta)/(cosec theta)+(cos theta)/(sec theta)=1

If ((1+cos theta+i sin theta)/(sin theta+i+i cos theta))^(4)=cos n theta+i sin n theta , then n=

If sin theta - cos theta = 3/5, sin theta cos theta = __________

HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. If A = [[ 2 ,-1] , [ 0 , 1 ]] and B=[[-3],[4]] then A B=

    Text Solution

    |

  2. If [[x+y] , [x-y]]=[[2,1] , [4,3]] [[1],[-2]] then (x,y)

    Text Solution

    |

  3. If A=[[sin theta , cos theta],[-cos theta , -sin theta]] then A^(2)=

    Text Solution

    |

  4. If the order of the matrix A=4xx 3, the order of B=4xx 5 and the order...

    Text Solution

    |

  5. [[x-y, 8], [ x+y, 9]] =[[2,8],[4,9]], then (x, y)

    Text Solution

    |

  6. Let A = [[1,2],[0,1]]. Then A^(n) =

    Text Solution

    |

  7. If A=[[2,3 ],[4,1]], B=[[1,2],[3,1]], then 2 A-3 B is

    Text Solution

    |

  8. If [[x,1],[-1,-y]]+[[y,1],[3,x]]=[[1,2],[2,1]] , then (x,y) =

    Text Solution

    |

  9. If A and B are two square matrices of same order then (A B)^(prime)=

    Text Solution

    |

  10. If A=[(3,5),(2,0)] and B = [(1,17),(0,-10)] then |AB| is equal to

    Text Solution

    |

  11. The matrix [[0, 5,-7], [-5,0,11],[7,-11,0]] is known as

    Text Solution

    |

  12. If in a square matrix A=(a(i j)) we have a(ji)=a(i j) for all i, j the...

    Text Solution

    |

  13. If A= [[4,x+2],[2x-3, x-1]] is symmetric then x=

    Text Solution

    |

  14. If A is a square matrix then A . A^(T) is

    Text Solution

    |

  15. If A+B=[[1,0],[1,1]] and A-2 B=[[-1,1],[0,1]] then A=

    Text Solution

    |

  16. If A=[[-1,2],[-2,1]], B=[[3,4],[2,-1]] and A+2 X=B, then X=

    Text Solution

    |

  17. If A=[(1,-3),(2,k)] and A^(2)-4A+10I=A, then k =

    Text Solution

    |

  18. If 2 A+3 B=[[2,-1,4],[3,2,5]] and A+2 B=[[5,0,3],[1,6,2]] then B=

    Text Solution

    |

  19. If O(A)=2xx3, O(B)=3xx2, and O(C )=3xx3 which one of the following is ...

    Text Solution

    |

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

    Text Solution

    |