Home
Class 12
MATHS
If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]...

If `A=[[0,-tan(alpha/2)],[tan(alpha/2),0]]` show that
`(I+A)` =`(I-A)[[cosalpha,-sinalpha],[sinalpha,cosalpha]]` where `I=[[1,0],[0,1]]`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MBD PUBLICATION|Exercise QUESTION TYPE|4 Videos
  • DIFFERENTIAL EQUATIONS

    MBD PUBLICATION|Exercise QUESTION BANK|87 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}]andA+A'=I , then find the value of alpha .

If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]] , show that for no values of alpha, A^2=B .

Prove the following : cos^2(alpha/2)(1-2cosalpha)^2+sin^2(alpha/2)(1+2cosalpha)^2 =1

If A=[[1,2,3],[3,-2,1],[4,2,1]] "show that" A^3-23A-40I=0

If A=[[1,-1,1,],[2,-1,0,],[1,0,0,]] ,then show that A^2=A^-1.

If A=[{:(1,-1,1),(2,-1,0),(1,0,0):}] then show that A^-1=A^2

If tanbeta=(n^2sinalpha cdot cosalpha)/(1-n^2sin^2alpha) then show that tan(alpha-beta)/(tanalpha)=1-n^2

If A_(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , then prove that A_(alpha)A_(beta)=A_(alpha+beta) .

If (1-e) tan^2frac{beta}{2}=(1+e)tan^2frac{alpha}{2} . prove that cosbeta=(cosalpha-e)/(1-ecosalpha)

MBD PUBLICATION-DETERMINATES-QUESTION BANK
  1. For what value of lamda the system of equations x+y+z=6, 4x+lamda y-...

    Text Solution

    |

  2. If A is a 3xx3 matrix and absA=2, then which matrix is represented by ...

    Text Solution

    |

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

    Text Solution

    |

  4. Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+...

    Text Solution

    |

  5. Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a...

    Text Solution

    |

  6. Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

    Text Solution

    |

  7. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

    Text Solution

    |

  8. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

    Text Solution

    |

  9. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

    Text Solution

    |

  10. Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] =a^3+b^...

    Text Solution

    |

  11. Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =...

    Text Solution

    |

  12. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

    Text Solution

    |

  13. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

    Text Solution

    |

  14. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

    Text Solution

    |

  15. Without expanding show that the following determinant is equal to Ax+B...

    Text Solution

    |

  16. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

    Text Solution

    |

  17. If a1, a2,........,an are in G.P. and ai gt 0 for every i, then find t...

    Text Solution

    |

  18. If f(x)=[[1+sin^2x,cos^2x,4sin2x],[sin^2x,1+cos^2x,4sin2x],[sin^2x,cos...

    Text Solution

    |

  19. If fr(x),gr(x),hr(x),r=1, 2, 3 are polynomials in x such that fr(a)=...

    Text Solution

    |

  20. If f(x)=[[cosx,sinx,cosx],[cos2x,sin2x,2cos2x],[cos3x,sin3x,3cos3x]] ...

    Text Solution

    |