Home
Class 12
MATHS
In any DeltaABC, prove that a^(3)cos(B-...

In any `DeltaABC`, prove that
`a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)=3abc`

Text Solution

Verified by Experts

The correct Answer is:
`therefore a^(3) cos (B-C) +b^(3) (C-A) +c^(3) cos (A-B) =3abc`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise SOLVED EXAMPLES|1 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

In any triangle ABC, prove that : a^3 sin (B-C)+ b^3 sin (C-A)+ c^3 sin (A-B)=0 .

In any triangle A B C , prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B)=(a^2+b^2)/(a^2+c^2)

In any DeltaABC prove by vectors that a^2=b^2+c^2-2 bc cos A.

In any triangle ABC, prove that : a (b cos C-c cos B) = b^2 -c^2 .

In any triangle ABC, prove that : a (cos C - cos B) = 2 (b-c) cos^2 frac (A)(2) .

In any triangle ABC, prove that : (a^2-b^2)/(cos A+cos B)+(b^2-c^2)/(cos B+cos C)+(c^2-a^2) /(cos C+cos A)=0 .

In any triangle ABC, prove that : sin frac (B-C)(2) = (b-c)/(a) cos frac (A)(2) .

In any triangle ABC, prove that : a cos frac (B-C)(2)= (b +c) sin frac (A)(2)= (b+c)cos frac (B+C)(2) .

In any DeltaABC prove by vectors that b^2=c^2+a^2-2 ca cos B.

In a DeltaABC, prove that: 2r le (a cot A+ b cot B+ c cot C)/(3)leR

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. In any DeltaABC, prove that a^(3)cos(B-C)+b^(3)cos(C-A)+c^(3)cos(A-B)...

    Text Solution

    |

  2. Prove that 2sin^2(pi/6) - sec^2(pi/3)= -7/2

    Text Solution

    |

  3. In a triangle the sum of two sides is x and the product of the same is...

    Text Solution

    |

  4. Consider a triangle A B C and let a , b and c denote the lengths of th...

    Text Solution

    |

  5. Solution of differential equation 2xy dy / dx = x^2 + 3y^2 is .

    Text Solution

    |

  6. Let PQR be a triangle of area Delta with a = 2, b = 7//2, and c = 5//2...

    Text Solution

    |

  7. If the angle A ,Ba n dC of a triangle are in an arithmetic propression...

    Text Solution

    |

  8. Let A B C be a triangle such that /A C B=pi/6 and let a , b and c deno...

    Text Solution

    |

  9. A triangle A B C with fixed base B C , the vertex A moves such that co...

    Text Solution

    |

  10. Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...

    Text Solution

    |

  11. A straight line through the vertex P of a triangle P Q R intersects th...

    Text Solution

    |

  12. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  13. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  14. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

    Text Solution

    |

  15. Internal bisector of /A of triangle ABC meets side BC at D. A line dra...

    Text Solution

    |

  16. One angle of an isosceles triangle is 120^0 and the radius of its incr...

    Text Solution

    |

  17. In Delta ABC, which one is true among the following ?

    Text Solution

    |

  18. Let a vertical tower A B have its end A on the level ground. Let C be ...

    Text Solution

    |

  19. ABCD is a trapezium such that AB and CD are parallel and BC bot CD. If...

    Text Solution

    |

  20. For a regular polygon, let r and R be the radii of the inscribed and t...

    Text Solution

    |

  21. In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...

    Text Solution

    |