Home
Class 12
MATHS
If a ,b ,and c are the sides of a triang...

If `a ,b ,and c` are the sides of a triangles and`A , B and C` are the angles opposites to `a ,b and c ,` respectively then `"Delta"=|a^2b s in A c s in A bs in A1cos A cs in A cos A1|` is independent of

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

Let a,b,c be the sides of a triangle ABC, a=2c,cos(A-C)+cos B=1. then the value of C is

If a,b,c are sides of a triangle and a^(2) + b^(2) = c^(2) , name the type of triangle.

If a , b , c are the sides of triangle , then the least value of (a)/(c+a-b)+(b)/(a+b-c)+(c )/(b+c-a) is

In a triangle ABC , if a,b,c are the sides opposite to angles A , B , C respectively, then the value of |{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}| is

In Delta ABC, (sin A (a - b cos C))/(sin C (c -b cos A))=

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a)/(c) sin 2C + (c)/(a) sin 2A is

In a right angle triangle ABC, right angle is at B ,If tan A=sqrt(3) , then find the value of (i) sin A cos C+ cos A sin C " "(ii) cos A cos C -sin A sin C

If the middle points of the sides B C ,C A , and A B of triangle A B C are (1,3),(5,7), and (-5,7), respectively, then find the equation of the side A Bdot

In a triangle ABC , a =2,b=3 and sin A = (2)/(3) then cos C=

If A , Ba n dC are the angels of a triangle, show that |-1+cos B cos C+cos B cos B cos C+cos A-1+cos A cos A-1+cos B-1+cos A-1|=0

CENGAGE-DETERMINANTS-All Questions
  1. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|a1a2a3 4 5a6a7a8a9|...

    Text Solution

    |

  2. Column I, Column II The value of the determinant |x+2x+3x+5x+4x+6x...

    Text Solution

    |

  3. If a ,b ,and c are the sides of a triangles andA , B and C are the ang...

    Text Solution

    |

  4. If f(x) is a polynomial of degree <3, prove that |1af(a)//(x-a)1bf(b)/...

    Text Solution

    |

  5. Prove that =|a c c-a +b c b b-c b+c a-b b-c 0 a-c x y z 1+x+y|=0 impli...

    Text Solution

    |

  6. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  7. Absolute value of sum of roots of the equation |x+22x+3 3x+4 2x+3 3x+4...

    Text Solution

    |

  8. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

    Text Solution

    |

  9. The product of all values of t , for which the system of equations (a-...

    Text Solution

    |

  10. Prove that for any A.P. a1, a2, a3, , then determinant |ap+a(p+m)+a(p...

    Text Solution

    |

  11. Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1]...

    Text Solution

    |

  12. If =|-x a bb-x a a b-x| , then a factor is a+b+x x^2-(a-b)+x+a^2+b...

    Text Solution

    |

  13. If g(x)=|a^(-x)e^(x loge a)x^2a^(-3x)e^(3x loge a)x^4a^(-5x)e^(5x loge...

    Text Solution

    |

  14. the sum of values of p for which the equations x+y+z=1x+2y +4z=p...

    Text Solution

    |

  15. The value of |alpha| for which the system of equation alphax+y+z=...

    Text Solution

    |

  16. Let D1=|a b a+b c d c+d a b a-b|a n dD2=|a c a+c b d b+d a c a+b+c| th...

    Text Solution

    |

  17. If |xx+y x+y+z2x3x+2y4x+3y+2z3x6x+3y 10 x+6y+3z|=64 , then the real va...

    Text Solution

    |

  18. If =|1 3costheta1s intheta1 3costheta1s intheta1| , then the value of ...

    Text Solution

    |

  19. If |x^n x^(n+2)x^(n+4)y^n y^(n+2)y^(n+4)z^n z^(n+2)z^(n+4)|=(1/(y^2)-1...

    Text Solution

    |

  20. The value of |2x1y1x1y2+x2y1x1y3+x3y1x1y2+x2y1 2x2y2x2y3+x3y2x1y3+x3y1...

    Text Solution

    |