Home
Class 12
MATHS
If A=[costhetaisinthetaisinthetacostheta...

If `A=[costhetaisinthetaisinthetacostheta]` , then prove by principle of mathematical induction that `A^n=[cosn\ thetaisinn\ thetaisinn\ thetacosn\ theta]` for all `n in N` .

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

If A=[[costheta,isintheta],[isintheta,costheta]], then prove by principal of mathematical induction that A^n=[[cosntheta, i sinn theta],[isin n theta, cos n theta]] for all n in NN .

Prove by the principle of mathematical induction that 2^ n >n for all n∈N.

Prove by the principle of mathematical induction that n<2^n"for all"n in Ndot

Using the principle of mathematical induction, prove that n<2^n for all n in N

Prove by the principle of Mathematical Induction that log x^(n)=nlogx , for all n in N .

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Prove by the principle of mathematical induction that: n(n+1)(2n+1) is divisible by 6 for all n in Ndot

Prove by the principle of mathematical induction that (n^5)/5+(n^3)/3+(7n)/(15) is a natural number for all n in Ndot

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If [[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all positive int...

    Text Solution

    |

  2. If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] ...

    Text Solution

    |

  3. If A=[costhetaisinthetaisinthetacostheta] , then prove by principle...

    Text Solution

    |

  4. If A=[cosalpha+sinalpha,sqrt(2)sinalpha; -sqrt(2)sinalpha,cosalpha-sin...

    Text Solution

    |

  5. If A=[1 1 1 0 1 1 0 0 1] , then use the principle of mathematical in...

    Text Solution

    |

  6. If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=...

    Text Solution

    |

  7. If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n)...

    Text Solution

    |

  8. If A is a square matrix, using mathematical induction prove that (A...

    Text Solution

    |

  9. A matrix X has a+b rows and a+2 columns while the matrix Y has b+1 ...

    Text Solution

    |

  10. Give examples of matrices A and B such that A B!=B A . (ii) A and B...

    Text Solution

    |

  11. Give examples of matrices A and B such that A B=O but B A!=O . (ii)...

    Text Solution

    |

  12. Let A and B be square matrices of the same order. Does (A+B)^2=A^2+...

    Text Solution

    |

  13. If A and B are square matrices of the same order, explain, why in g...

    Text Solution

    |

  14. Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...

    Text Solution

    |

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

    Text Solution

    |

  16. Let A=[[1 ,1, 1],[ 3, 3, 3]] , B=[[3,1], [5, 2],[-2, 4]] and C=[[4,2],...

    Text Solution

    |

  17. Three shopkeepers A ,\ B\ a n d\ C go to a store to buy stationary....

    Text Solution

    |

  18. The cooperative stores of a particular school has 10 dozen physics ...

    Text Solution

    |

  19. In a legislative assembly election, a political group hired a public...

    Text Solution

    |

  20. A trust fund has Rs. 30000 that must be invested in two different ty...

    Text Solution

    |