Home
Class 12
MATHS
Prove that the determinant {:[( x, sin ...

Prove that the determinant ` {:[( x, sin theta ,cos theta ),( -sin theta , -x , 1),( cos theta , 1,x) ]:}` is independent of ` theta.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

Prove that the determinant Delta =|{:(x,,sintheta,,cos theta),(-sin theta,,-x,,1),(cos theta,,1,,x):}| is independent of theta .

determinant |"cos theta sin theta -sin theta cos theta

If tan theta = 1/b , then ( a sin theta - b cos theta )/( a sin theta + b cos theta) is

Prove that sqrt((sec theta -1)/( sec theta +1))=(1- cos theta )/( sin theta )

Prove that (cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1)

the solution of sin ^3 theta cos theta - sin theta cos^3 theta = 1/4 is

If A=[{:(cos theta, sin theta),(-sin theta, cos theta):}] then "A A"^(T) is :

Prove than: sec theta + tan theta = (cos theta )/(1 - sin theta)

CENGAGE-DETERMINANTS-All Questions
  1. A determinant of second order is made with the elements 0 and 1. Fi...

    Text Solution

    |

  2. If a ,b , c are nonzero real numbers such that |b cc a a b c a a bb c ...

    Text Solution

    |

  3. Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin thet...

    Text Solution

    |

  4. Consider the determinant f(x)=|0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|dot...

    Text Solution

    |

  5. Find the value of |1 2 4-1 3 0 4 1 0|

    Text Solution

    |

  6. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

    Text Solution

    |

  7. Each question has four choices a, b, c and d, out of which only one is...

    Text Solution

    |

  8. If a ,b ,c in R , then find the number of real roots of the equat...

    Text Solution

    |

  9. Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by ...

    Text Solution

    |

  10. Without expanding at any stage, prove that the value of each of the...

    Text Solution

    |

  11. If a,b,c are all positive, and are p^(th), q^(th) and r^(th) terms of ...

    Text Solution

    |

  12. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

    Text Solution

    |

  13. The value of the determinant of n^(t h) order, being given by |x1 11x1...

    Text Solution

    |

  14. Solve the equation {:[( x+a,x,x),(x,x+a,x),(x,x,x+a) ]:}=0,ane 0

    Text Solution

    |

  15. If a1b1, c1,a2b2c2a n da3b3c3 are three digit even natural numbers and...

    Text Solution

    |

  16. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

    Text Solution

    |

  17. The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]|,w h e r ex ,y ,z are...

    Text Solution

    |

  18. Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+...

    Text Solution

    |

  19. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

    Text Solution

    |

  20. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

    Text Solution

    |