Home
Class 12
MATHS
If A = [(cos theta, sin theta),(-sin the...

If `A = [(cos theta, sin theta),(-sin theta, cos theta)]` then show that for all the positive integers n, `A^(n) = [(cos n theta,sin n theta),(-sin n theta,cos n theta)]`.

A

`[(cos n theta, sin n theta),(-sin n theta, cos n theta)]`

B

`[(cos^(n) theta, sin^(n) theta),((-1)^(n)sin^(n) theta, cos^(n) theta)]`

C

`[(n cos theta, n sin theta),(-n sin theta, n cos theta)]`

D

none

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B MCQ (DETERMINANTS)|189 Videos

  • MATRICES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1C MCQ (INVERSE MATRIX)|88 Videos

  • MATRICES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 MCQ (SPECIAL TYPES QUESTIONS) SET -4|8 Videos

  • MATHEMATICAL REASONING [APPENDIX - 4]

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise|150 Videos

  • MEASURES OF DISPERSION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE-2 ( SET -4)|2 Videos

Similar Questions

Explore conceptually related problems

If A=[(-cos theta, sin theta),(sin theta, cos theta)] then IAI=

If A=[(cos theta, sin theta),(- sin theta, cos theta)] then lim_(nto oo)1/n A^(n) is

The inverse of A=[( cos theta, sin theta),(-sin theta, cos theta)] is

If cos m theta = sin n theta , then theta =

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

If 1+sin^(2)theta = 3 sin theta cos theta , then theta =

If the matrix [(cos theta, sin theta, 0),(sin theta, cos theta, 0),(0,0,1)] is singular then theta=

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

If cos theta - sin theta = sqrt(2) sin theta " then " cos theta + sin theta =

DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1A MCQ (ALGEBRA OF MATRICES)
  1. If A=[(1,1,0),(0,1,1),(0,0,1)] then A^(2)=

    Text Solution

    |

  2. if n is a positive integer and A=[(a,0,0),(0,b,0),(0,0,c)] then A^(n) ...

    Text Solution

    |

  3. If A = [(cos theta, sin theta),(-sin theta, cos theta)] then show that...

    Text Solution

    |

  4. If A=[(cos theta, sin theta),(- sin theta, cos theta)] then lim(nto oo...

    Text Solution

    |

  5. If A=[(-cos theta, sin theta),(sin theta, cos theta)] then IAI=

    Text Solution

    |

  6. If A=[(cos^(2) alpha, cos alpha sin alpha),(cos alpha sin alpha,sin^(2...

    Text Solution

    |

  7. If alpha-beta=(2n+1)(pi)/2, n epsilon Z then [(cos^(2) alpha, cos alph...

    Text Solution

    |

  8. If A(alpha)=[(cos alpha, sin alpha),(-sin alpha, cos alpha)], then A(a...

    Text Solution

    |

  9. If A=[(a,b),(c,d)],I=[(1,0),(0,1)] then A^(2)-(a+d)A=

    Text Solution

    |

  10. If A=[(0,c,-b),(-c,0,a),(b,-a,0)] then A^(3)=

    Text Solution

    |

  11. If A=[(1,1,3),(5,2,6),(-2,-1,-3)] then A^(3)=

    Text Solution

    |

  12. If A=[(1,1,-2),(0,1,4),(2,3,1)] then A^(3)-3A^(2)-5A=

    Text Solution

    |

  13. A=[{:(1,2,2),(2,1,2),(2,2,1):}], then A^(3) - 4A^(2) -6A is equal to

    Text Solution

    |

  14. If A=[(4,2),(-1,1)] then (A-21) (A-3I)=

    Text Solution

    |

  15. If A=[(8,-6,2),(-6,7,-4),(2,-4,3)] then A(A-3I)(A-15I)=

    Text Solution

    |

  16. If A=[(1,0,0),(0,2,1),(1,0,3)] then (A-I)(A-2I)(A-3I)=

    Text Solution

    |

  17. If A=[(1,3),(3,4)] and A^(2)-kA-5I(2)=O then k=

    Text Solution

    |

  18. If A=[(-8,5),(2,4)] satisfies the equation f(x)=x^(2)+4x-p=0 then p=

    Text Solution

    |

  19. If ((3,-2),(-1,2))((x),(y))=((11),(-5)), then 3x+7y=

    Text Solution

    |

  20. If [(1,-tan theta),( tan theta,1)][(1,tan theta),(-tan theta, 1)]^-1=[...

    Text Solution

    |