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

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos
  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 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)

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. A variable plane is at a constant distance p from the origin and meets...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Find the probability distribution of number of doublets in four throws...

    Text Solution

    |

  5. What is the value of int0^picos^(101)xdx?

    Text Solution

    |

  6. If f(x)={(3x+2,xle0),(2-3x,xgt0):}

    Text Solution

    |

  7. What is the equation of the plane |r to y-axis and passing through(2,-...

    Text Solution

    |

  8. Find least non negative integer r such that 7xx13xx23xx413 -= r "(mod ...

    Text Solution

    |

  9. For a 2xx2 matrix A,if AxxadjA=[(10,0),(0,10)]then what is the value o...

    Text Solution

    |

  10. Write the Order and degree of the differential equation whose general ...

    Text Solution

    |

  11. With 4 different elements how many different determinant of order 2 ca...

    Text Solution

    |

  12. What is the value of a so that 6hati+2hatj-3hatk and hati-4hatj+ahatk...

    Text Solution

    |

  13. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

    Text Solution

    |

  14. Find the feasible solution region of the following system:-x+yge-1,x+y...

    Text Solution

    |

  15. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

    Text Solution

    |

  16. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

    Text Solution

    |

  17. If A+B+C=pi,then show that Abs((-1,cosC,cosB),(cosC,-1,cosA),(cosB,cos...

    Text Solution

    |

  18. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

    Text Solution

    |

  19. If A=[(1,2),(2,3),(3,4)]and B=[(2,3,0),(1,2,3)],then verify that (AB)^...

    Text Solution

    |

  20. Find A^-1 if A=[(4,-1),(2,3)]

    Text Solution

    |