Home
Class 11
MATHS
If in a DeltaABC, sin^3A+sin^3B+sin^3C=3...

If in a `DeltaABC,` `sin^3A+sin^3B+sin^3C=3sinA.sinB.sinC,`then find the value of determinant,`abs[(a,b,c) ,(b,c,a),(c,a,b)]`

Text Solution

Verified by Experts

`abs[(a,b,c),(b,c,a),(c,a,b)]=0`
Promotional Banner

Topper's Solved these Questions

  • SETS AND RELATIONS

    PATHFINDER|Exercise QUESTION BANK|56 Videos

  • STATISTICS

    PATHFINDER|Exercise QUESTION BANK|45 Videos

Similar Questions

Explore conceptually related problems

In a DeltaABC,sinA/sinC=sin(A-B)/sin(B-C) then

If in a triangle ABC ,(sin A+sin B +sin C)(sinA+sinB-sin C)=3sinAsinB then angle C is equal to

Prove that sin2A + sin2B + sin2C = 4sinA · sinB · sin C

In triangle A B C ,(sinA+sinB+sinC)/(sinA+sinB-sinC) is equal to

In a triangle ABC, (sin A+ sin B+ sin C) (sin A+sin B-sinC)= 3 sin A sin B, then which one of the following is correct ?

If sinA + sinB = 2, then which of the following is the value of sin (A + B)?

If in Delta ABC , Prove that, a^2 sin(B-C)= (b^2-c^2)sinA

In any triangle ABC, prove that sin^3Acos(B-C)+sin^3Bcos(C-A)+sin^3Ccos(A-B) = 3sinAsinBsinC

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

If in a triangle ABC, b sin B = c sin C, then the triangle is-

PATHFINDER-SOLUTION OF TRIANGLE AND HEIGHT AND DISTANCE-QUESTION BANK
  1. prove that cosA +cosB+cosC=1+r/R.

    Text Solution

    |

  2. The sides of a triangle are x^2+3x+3,2x+3,x^2+2x. Find the greatest a...

    Text Solution

    |

  3. If P1,P2,P3 be the altitudes of a triangle from the vertices A,B,C Res...

    Text Solution

    |

  4. If in triangleABC ,a^4+b^4+c^4=2c^2(a^2+b^2) then find angleC

    Text Solution

    |

  5. Let h1,h2,h3 be the altitudes of the DeltaABC and let the inradius be ...

    Text Solution

    |

  6. For any triangle ABC, find the value of (bc cos^2(A/2)+cacos^2(B/2)+a...

    Text Solution

    |

  7. If in a DeltaABC, sin^3A+sin^3B+sin^3C=3sinA.sinB.sinC,then find the v...

    Text Solution

    |

  8. AD is a median of the DeltaABC.If AE and AFare medians of the triangle...

    Text Solution

    |

  9. In a triangle DeltaXYZ, let a,b and c be the lengths of the sides opp...

    Text Solution

    |

  10. In a triangle DeltaXYZ, let a, b, and c be the length of the sides opp...

    Text Solution

    |

  11. If the angles of elevation of the top of a water from three collinear ...

    Text Solution

    |

  12. If in a triangle DeltaABC,a^2cos^2A-b^2-c^2=0, then

    Text Solution

    |

  13. In a triangle ABC,angleC=90^@, r and R are the inradius and circumra...

    Text Solution

    |

  14. A bird is sitting on the top of a vertical pole 20 m high and its elev...

    Text Solution

    |

  15. In a DeltaABC, tanA and tanB are the roots of pq(x^2+1)=r^2x. Then Del...

    Text Solution

    |

  16. In a DeltaABC, a,b,c are the sides of the triangle opposite to the ang...

    Text Solution

    |

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

    Text Solution

    |

  18. Let p,q,r be the sides opposite to the angles P,Q,R respectively in a ...

    Text Solution

    |

  19. Let p,q,r be the altitudes of a triangle with area s and perimeter 2t....

    Text Solution

    |

  20. If in a triangle ABC, sinA, sinB,sinC are in A.P., then

    Text Solution

    |