Home
Class 12
MATHS
If in a Delta ABC, sin ^(3) A + sin ^(3)...

If in a `Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C`
`=3 sin A .Sin B. sin C,` then find the valueof determinant
`|{:(a,b,c),(b,c,a),(c,a,b):}|.`

A

0

B

`(a+b+c)^(3)`

C

(a+b+c)(ab+bc+ca)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|55 Videos

  • PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • PLANE AND STRAIGHT LINE IN SPACE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|31 Videos

  • REAL FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos

Similar Questions

Explore conceptually related problems

In any Delta ABC, sum a(sin B - sin C) =

In a Delta ABC sin Asin B sin C <= (3sqrt3)/8

In any Delta ABC, sum a sin (B -C) =

In a Delta ABC, show that 2R^(2) sin A sin B sin C=Delta.

In DeltaABC, if sin^2 A+ sin^2 B = sin^2 C , then the triangle is

If in a triangle ABC, 3 sin A = 6 sin B=2sqrt3sin C , then the angle A is

If in a triangle ABC, 3 sin A = 6 sin B=2sqrt3sin C , then the angle A is

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

If A+B+C=pi , show that : 1/2 sum sin^2 A (sin 2B+sin 2C) = 3 sin A sin B sin C .

If in a DeltaABC, sin A, sin B, sin C are in A.P., show that 3 tan, A/2 tan, C/2 = 1

OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Exercise
  1. If the sides of the triangle are the roots of the equation x^(3)-2x^(...

    Text Solution

    |

  2. If AD, BE and CF are the medians of a Delta ABC, then evaluate (AD^(2)...

    Text Solution

    |

  3. If a DeltaABC is right angled at B, then the diameter of the incircle ...

    Text Solution

    |

  4. If a^(2),b^(2),c^(2) are in A.P.,then which of the following is also i...

    Text Solution

    |

  5. If in a Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C =3 sin A .Sin...

    Text Solution

    |

  6. If the ex-radii of a triangle are in H.P.,then the corresponding sides...

    Text Solution

    |

  7. If I is the incentre of a !ABC , then IA:IB:IC is equal to

    Text Solution

    |

  8. In a triangle ABC ,the HM of the ex-radii is equal to

    Text Solution

    |

  9. In a DeltaABC if r(1):r(2):r(3)=2:4:6, then a:b:c =

    Text Solution

    |

  10. If in a !ABC,angleA=pi//3 and AD is a median , then

    Text Solution

    |

  11. In a triangle ABC cos^(2)A/2+cos^(2)B/2+cos^(2)C/2=

    Text Solution

    |

  12. The base of a triangle is 80cm and one of the base angles is 60^(@).If...

    Text Solution

    |

  13. In a DeltaABC if r(1)=16,r(2)=48 and r(3)=24, then its in-radius ,is

    Text Solution

    |

  14. In a △ ABC if a =26, b= 30 and cos C =63/65, then r(2) =

    Text Solution

    |

  15. In a triangle ABC if sides a = 13, b =14 and c = 15, then reciprocals...

    Text Solution

    |

  16. In a A B C , ifsinAa n dsinB are the roots of the equation c^2x^2-c(a...

    Text Solution

    |

  17. If a , b , c denote the sides of a !ABC such that the equation x^(2)+...

    Text Solution

    |

  18. In a Delta ABC if b+c=2a and /A=60^@ then Delta ABC is

    Text Solution

    |

  19. In a Delta ABC, if b=20, c=21and sin A =3/5, then the value of a is

    Text Solution

    |

  20. Let A, B and C are the angles of a plain triangle and tan(A/2)=1/3...

    Text Solution

    |