Home
Class 12
MATHS
If A=[{:(costheta,sintheta),(-sintheta,...

If `A=[{:(costheta,sintheta),(-sintheta,costheta):}]`, then prove that `A^(n)=[{:(cosntheta,sinntheta),(-sinntheta,cosn theta):}], n inN`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

Simplify , costheta[{:(costheta,sintheta),(-sintheta,costheta):}]+sintheta[{:(sintheta,-costheta),(costheta,sintheta):}]

If M( theta)=[{:(cos theta,sintheta),(-sintheta, cos theta):}] then show that M(x)M(y)=M(x+y) .

Evaluate the following determinants. [[costheta,sintheta],[sintheta,costheta]]

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

If x = 2costheta-cos2theta , y = 2sintheta-sin2theta then find d^(2)y/dx^(2) at theta =pi/2 .

Prove the following : (sintheta+sin3theta+sin5theta+sin7theta)/(costheta+cos3theta+cos5theta+cos7theta) = tan4theta

Show that ((1+sintheta+icostheta)/(1+sintheta-icostheta))^n =cos((npi)/2-ntheta)+isin((npi)/2-ntheta)

If x+1/x=2cos theta,"Show that"x^n+1/x^n=2cos n theta

For ____value of theta , sintheta+costheta=sqrt2

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Express A=[[2,-2,-4],[-1,3,4],[1,-2,-3]] as the sum of a symmetric and...

    Text Solution

    |

  2. Using the properties of determinants, show that abs[[1+a^2-b^2,2ab,-2b...

    Text Solution

    |

  3. If A=[{:(costheta,sintheta),(-sintheta,costheta):}], then prove that ...

    Text Solution

    |

  4. Find the minimum value of abs[[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+...

    Text Solution

    |

  5. Find the values of x and y such that [{:(3x+7,5),(y+1, 2-3x):}]=[{:(0,...

    Text Solution

    |

  6. Discuss the continuity of the function defined by f(x)={[x+1, if xle1]...

    Text Solution

    |

  7. Differentiate the functions w.r.t x x^(xcosx)+frac[x^2+1][x^2-1]

    Text Solution

    |

  8. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

    Text Solution

    |

  9. Find the intervals in which the function f given by f(x)=sinx+cosx, 0l...

    Text Solution

    |

  10. If x=(sin^(3)t)/(sqrt(cos2t)) and y=(cos^(3)t)/(sqrt(cos2t)), then fin...

    Text Solution

    |

  11. Find the integral intfrac[x^3sin(tan^(-1)x^4)][1+x^8]dx

    Text Solution

    |

  12. Find the integral intfrac[x+3][(5-4x+x^2)]dx

    Text Solution

    |

  13. Evaluate int(0)^(pi//2)logsinxdx.

    Text Solution

    |

  14. Form the differential equation of the family of all circles of radius ...

    Text Solution

    |

  15. Solve the differential equation frac[dy][dx]=log(x+1)

    Text Solution

    |

  16. The two adjacent sides of a parallelogram are 2hati-4hatj+5hatk and ha...

    Text Solution

    |

  17. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

    Text Solution

    |

  18. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

    Text Solution

    |

  19. Prove by vector method that in a parallelogram, the line joining a ve...

    Text Solution

    |

  20. If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^...

    Text Solution

    |