Home
Class 11
MATHS
In any triangle A B C , prove that follo...

In any triangle `A B C` , prove that following: `\ bsinB-csinC=asin(B-C)`

Text Solution

Verified by Experts

`b sin B-c sin C=a sin (B-c)`

By Sine rule.

`frac{a}{sin A}=frac{b}{sin B}=frac{c}{sin C}=k`

`a=k sin A, b=k sin B, C=k sin C`

...
Promotional Banner

Topper's Solved these Questions

  • SETS

    RD SHARMA|Exercise Solved Examples And Exercises|218 Videos
  • SOME SPECIAL SERIES

    RD SHARMA|Exercise Solved Examples And Exercises|69 Videos

Similar Questions

Explore conceptually related problems

In any triangle ABC, prove that following: quad b cos B+c cos C=acos(B-C)

In any triangle ABC, prove that following: a(s in B-s in C)+b(s in C-s in A)+c(s in A-s in B)=0

In DeltaABC , prove that: bsinB-c sinC=asin(B-C)

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

In any triangle ABC, prove that following: a^(2)sin(B-C)=(b^(2)-c^(2))s in A

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

In any triangle ABC, prove that following: (a^(2)sin(B-C))/(s in A)+(b^(2)sin(C-A))/(s in B)+(c^(2)sin(A-B))/(s in C)=0

In any triangle ABC, prove that following: (a^(2)-c^(2))/(b^(2))=(sin(A-C))/(sin(A+C))

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

In any triangle ABC, prove that following: quad a cos A=b cos B=c cos C=2b sin A sin C=2c sin A sin B

RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
  1. In any triangle A B C , prove that following: sin((B-C)/2)=(b-c)/acosA...

    Text Solution

    |

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

    Text Solution

    |

  3. In any triangle A B C , prove that following: \ bsinB-csinC=asin(B-C)

    Text Solution

    |

  4. In any triangle A B C , prove that following: \ \ a^2sin(B-C)=(b^2-c^2...

    Text Solution

    |

  5. In any triangle A B C , prove that following: \ a(sin B-sin C)+b(sin C...

    Text Solution

    |

  6. In any triangle A B C , prove that following: \ (a^2"sin"(B-C))/(sin A...

    Text Solution

    |

  7. In any triangle A B C , prove that following: \ \ bcosB+c\ cos\ C=a co...

    Text Solution

    |

  8. In any triangle A B C , prove that following: \ (cos^2B-cos^2C)/(b+c)+...

    Text Solution

    |

  9. In any triangle A B C , prove that following: \ \ asin(A/2)sin((B-C)/2...

    Text Solution

    |

  10. In any triangle A B C , prove that following: \ \ acosA+bcosB+c\ cos C...

    Text Solution

    |

  11. In any triangle A B C , prove that following: \ a\ (cosB cos C+cos A)=...

    Text Solution

    |

  12. In a Delta A B C ,\ ifsin^2A+sin^2B=sin^2C , show that the triangle i...

    Text Solution

    |

  13. The upper part of a tree broken over by the wind makes an angle of 30^...

    Text Solution

    |

  14. If the sides of a DeltaA B C\ are a=4,\ b=6\ a n d\ c=8, show that 4...

    Text Solution

    |

  15. In any Delta A B C , prove that: a(b\ cos C-c cosB)=b^2-c^2

    Text Solution

    |

  16. In any Delta A B C , prove that: (cos A)/a+(cos B)/b+(cos C)/c=(a^2+b...

    Text Solution

    |

  17. In any Delta A B C , prove that: 2(bc cosA+cacosB+a bcosC)=a^2+b^2+c^...

    Text Solution

    |

  18. In a Delta A B C , prove that: (b^2-c^2)cotA+(c^2-a^2)cot B+(a^2-b^2)...

    Text Solution

    |

  19. In a Delta A B C , prove that: ((b^2-c^2)/(a^2))sin2A+((c^2-a^2)/(b^2)...

    Text Solution

    |

  20. In any DeltaA B C prove that acosA+bcosB+c cosC=(8Delta^2)/(a b c)dot

    Text Solution

    |