Home
Class 12
MATHS
If A=[[costheta,sintheta],[-sintheta,cos...

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

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|128 Videos
  • RELATIONS AND FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|86 Videos

Similar Questions

Explore conceptually related problems

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 .

If A=[(costheta,sintheta),(-sintheta,costheta)] Find A^2

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

Simplify costheta[[costheta, sin theta],[-sintheta, costheta]]+sintheta[[sintheta, -costheta],[costheta, sintheta]]

Prove that (1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cottheta

Solve sin2theta+costheta=0

Prove that cos^2theta=(1+cos2theta)/2

Prove that (cos2theta)/(1+sin2theta)=tan(pi//4-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]]

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)

A N EXCEL PUBLICATION-PROBABILITY-QUESTION BANK
  1. If tan^(-1) ((x-1)/(x-2)) + tan^(-1) ((x+1)/(x+2)) = pi/4. then find t...

    Text Solution

    |

  2. The value of k such that matrix [[1,k],[-k,1]] is symmetric if

    Text Solution

    |

  3. If A=[[costheta,sintheta],[-sintheta,costheta]] then prove that A^2...

    Text Solution

    |

  4. If A=[[1,3],[4,1]] , then find abs(3A^T)

    Text Solution

    |

  5. If A=[[a,1],[1,0]] is such that A^2=I then a equals

    Text Solution

    |

  6. Solve the system of equations x-y+z=4,2x+y-3z=0,x+y+z=2 Using matr...

    Text Solution

    |

  7. Find the values of a and b such that the function f(x)={(5a,x le 0) ...

    Text Solution

    |

  8. Find dy/dx if (sinx)^(cosy) = (cosy)^(sinx)

    Text Solution

    |

  9. The slope of the normal to the curve, y^2=4x at (1,2) is

    Text Solution

    |

  10. Find the intervals in which the function 2x^3+9x^2+12x-1 is strictly i...

    Text Solution

    |

  11. The rate of change of volume of a sphere with respect to its radius wh...

    Text Solution

    |

  12. Find two positive numbers whose sum is 16 and the sum of whose Cubes i...

    Text Solution

    |

  13. Find the following: int 1/(x(x^7+1))dx

    Text Solution

    |

  14. Find the following: int1^4abs[x-2]dx

    Text Solution

    |

  15. Find int0^(pi/2) logsinxdx

    Text Solution

    |

  16. Evaluateint0^4x^2dx as the limit of a sum.

    Text Solution

    |

  17. Area bounded by the curves y=cosx ,x=pi/2, x=0, y=0 is

    Text Solution

    |

  18. Find the area of the region bounded by the y^2=4ax and x^2=4ay, a>0

    Text Solution

    |

  19. The order of the differential equation x^2 (d^2y)/(dx^2)=1+(dy/dx)^3 i...

    Text Solution

    |

  20. Find the particular solution of the differential equation (1+x^2)(...

    Text Solution

    |