Home
Class 12
MATHS
If A=((cosx,sinx),(-sinx,cosx)) then pro...

If `A=((cosx,sinx),(-sinx,cosx))` then prove that `A^n=((cosnx,sin nx),(-sin nx,cosnx)` for all positive integers n.

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    MODERN PUBLICATION|Exercise EXERCISE|12 Videos

  • RELATION AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|47 Videos

Similar Questions

Explore conceptually related problems

If y=tan^(-1)(cosx/(1+sinx)), then prove that dy/dx=-1/2

Write the value of int(cosx-sinx)/(sinx+cosx)dx .

If y=5cosx-3sinx ,then prove that (d^(2)y)/(dx^(2))+y=0

Prove that int_0^(pi/2)(sin^nx)/(sin^nx+cos^nx)dx=pi/4

Evaluate: int(3+2cosx+4sinx)/(2sinx+cosx+3) dx

If y =(cosx+sinx)/cosx, then what is dy/dx ?

If y=x^(sinx)+(sinx)^(cosx) , then find (dy)/(dx) .

If f(x)=[{:(cosx,-sinx,0),(sinx,cosx,0),(0,0,1):}] , then show that f(x)*f(y)=f(x+y) .

MODERN PUBLICATION-MATRICES-PROBLEM
  1. What is A+B if A=((1,2),(3,-1)) B=((0,-1),(-2,1)) ?

    Text Solution

    |

  2. Give an example of a unit matrix.

    Text Solution

    |

  3. Express A=((1,2),(2,3) as the sum of a symmetric and a skew symmetric ...

    Text Solution

    |

  4. If ((x(1),x(2)),((y(1),y(2))-((2,3),(0,1)),=((3,5),(1,2)) then find x(...

    Text Solution

    |

  5. Construct a 2 x 3 matrix having elements defined by a(ij)=i-j.

    Text Solution

    |

  6. Find x,y if A=A^’ where A=((5,x),(y,0))

    Text Solution

    |

  7. If A=((3,0,0),(0.3,0)(0,0,3) then find A^2.

    Text Solution

    |

  8. Can a matrix be constructed by taking 29 elements?

    Text Solution

    |

  9. Verify that [AB]^T = B^T A^T whereA=[[1,2],[2,3],[3,4]]=[[2,3,0],[1,2,...

    Text Solution

    |

  10. There are two families A and B. There are 4 men, 6 women and 2 childre...

    Text Solution

    |

  11. A trust fund has Rs. 50,000 that is to be invested in two types of ...

    Text Solution

    |

  12. Prove that a unit matrix is its own inverse. Is the converse true ?

    Text Solution

    |

  13. Express as a sum of a symmetric and skew symmetric matrix. [(2,-1,3),(...

    Text Solution

    |

  14. Express as a sum of a symmetric and skew symmetric matrix. [(x,a,b),(a...

    Text Solution

    |

  15. Show that A =((2,-3)(3,4)) satisfies equation x^2-6x+17=0. Hence find ...

    Text Solution

    |

  16. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

    Text Solution

    |

  17. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

    Text Solution

    |

  18. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

    Text Solution

    |