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

If `A=[[cos theta, sin theta],[ -sin theta, cos theta]]`, then prove that `A^n=[[cos ntheta, sinn theta],[ -sin n theta, cos n theta]]`, `n in N`.

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    V PUBLICATION|Exercise QUESTION BANK|39 Videos

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|132 Videos

Similar Questions

Explore conceptually related problems

If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2=[[cos2theta,sin2theta],[-sin2theta,cos2theta]]

Evaluate |[cos theta, -sin theta], [sin theta, cos theta]|

Show that [[1 , -tan theta ],[ tan theta, 1]][[1, tan theta],[ -tan theta, 1]]^(-1)=[[cos 2 theta, -sin 2 theta],[ sin 2 theta, cos 2 theta]]

If cos theta+sin theta=sqrt(2) cos theta ,then show that cos theta-sin theta=sqrt(2) sin theta

Solve sqrt 2+sin theta=cos theta .

Given that tantheta=a/b find sin2theta and cos2theta

Prove that sin (3theta)/(1+2cos 2theta)=sin theta .

The parametric form of the ellipse 4 (x +1) ^(2) + (y-1) ^(2) = 4 is a) x = cos theta -1 , y =2 sin theta -1 b) x = 2 cos theta-1 , y =2 sin theta -1 c) x = cos theta - 1, y = 2 sin theta + 1 d) x = cos theta +1, y =2 sin theta +1

V PUBLICATION-MATRICES-QUESTION BANK
  1. Find the inverse of the following using elementary transformations[[2,...

    Text Solution

    |

  2. Find the inverse of the following matrices if it exists.[[2, 1],[ 4,...

    Text Solution

    |

  3. If A=[[cos theta, sin theta],[ -sin theta, cos theta]], then prove ...

    Text Solution

    |

  4. If A and B are symmetric matrices of the same order, then show that A ...

    Text Solution

    |

  5. Let A=[[2 , -1],[3 , 4]], B=[[5, 2],[ 7, 4]] , C=[[2, 5],[ 3, 8]...

    Text Solution

    |

  6. If A=[[1 , 1, 1],[ 1, 1, 1],[ 1, 1 , 1]], prove that A^n=[[3^(n-...

    Text Solution

    |

  7. if A=[[3, -4],[ 1, (-1)]], then prove that A^n=[[1+2 n, -4 n ],[n...

    Text Solution

    |

  8. If A and B are symmetric matrices, prove that A B-B A is a skew symmet...

    Text Solution

    |

  9. Show that the matrix B^' A B is symmetric or skew symmetric according ...

    Text Solution

    |

  10. Find the values of x, y, z, if the matrix A=[[0, 2 y, z],[ x, y, ...

    Text Solution

    |

  11. For what values of x:[[1, 2, 1]] [[1, 2, 0],[ 2, 0, 1],[ 1, 0...

    Text Solution

    |

  12. If A=[[3,1],[-1,2]] then Hence show that A^2-5A+7I=0

    Text Solution

    |

  13. Find x, if [[x,-5,-1]] [[1, 0, 2],[ 0, 2, 1],[ 2, 0, 3]][[x],[...

    Text Solution

    |

  14. Find the matrix X so that X[[1 , 2, 3],[ 4, 5, 6]]=[[-7, -8, -9]...

    Text Solution

    |

  15. If A and B are square matrices of the same order such that A B=B A,the...

    Text Solution

    |

  16. If A=[[alpha ,beta],[ gamma , -alpha]] is such that A^2=I, then A) ...

    Text Solution

    |

  17. If the matrix A is both symmetric and skew symmetric, then: A)A is a d...

    Text Solution

    |

  18. If A is a square matrix such that A^2=A, then (I+A)^3-7 A is equal to ...

    Text Solution

    |

  19. Construct a m xx n matrix A=[[a(ij)]] whose elements a(ij) is given by...

    Text Solution

    |

  20. If [[a+b ,2],[ 5 , a b]]=[[6 , 2],[ 5, 8]], find the values of a an...

    Text Solution

    |