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

  • DETERMINANTS

    NCERT TAMIL|Exercise EXERCISE 4.6|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE|18 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)

NCERT TAMIL-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin thet...

    Text Solution

    |

  2. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

    Text Solution

    |

  3. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

    Text Solution

    |

  4. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

    Text Solution

    |

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

    Text Solution

    |

  6. Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2...

    Text Solution

    |

  7. If A^(-1) ={:[( 3,-1,1),(-15,6,-5),(5,-2,2) ]:}and B= {:[( 1,2,-2),( -...

    Text Solution

    |

  8. Let A = {:[( 1,2,1),(2,3,1),(1,1,5) ]:} Verify that (A^(-1) )^(-1) =...

    Text Solution

    |

  9. Evaluate {:[( x,y , x+y),( y,x+y,x),( x+y,x,y)]:}

    Text Solution

    |

  10. Evaluate {:[(1,x,y),( 1,x+y,y),( 1,x,x+y)]:}

    Text Solution

    |

  11. Using properties of determinants in Exercises prove that : {:[( alph...

    Text Solution

    |

  12. {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(3)),( z,z^(2) , 1+pz^(3)...

    Text Solution

    |

  13. solve {:[( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) ]:} = 3( a+...

    Text Solution

    |

  14. {:[( 1,1+p,1+p+q),( 2,3+2p,4+3p+2q),( 3,6+3p,10+6p+3q)]:}=1

    Text Solution

    |

  15. Without expanding evaluate the determinant |(sinalpha,cosalpha,sin(alp...

    Text Solution

    |

  16. Solve system of linear equations , using matrix method 2x+ 3y + ...

    Text Solution

    |

  17. If a,b,c are in A.P. then the determinant {:[( x+2,x+3,x+2a),( x+3,...

    Text Solution

    |

  18. If x,y,z are nonzero real number , then the inverse of matrix A= {:[( ...

    Text Solution

    |

  19. Let A={:[( 1,sin theta , 1),( -sin theta , 1, sin theta ),( -1 ,-sin ...

    Text Solution

    |