Home
Class 11
MATHS
In any Delta A B C , prove that: a(b\ c...

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

Text Solution

Verified by Experts

L.H.S. =`a(b cos C-c cos B) `
`=a{b(frac{a^{2}+b^{2}-c^{2}}{2 a b})-c(frac{a^{2}+c^{2}-b^{2}}{2 a c})}] ldots`[ By cosine rule]
`=frac{(a^{2}+b^{2}-c^{2})-(a^{2}+c^{2}-b^{2})}{2} `
`=frac{1}{2}(2 b^{2}-2 c^{2}) `
`=b^{2}-c^{2} `
= R.H.S.
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 Delta ABC, prove that :a(b cos C-c cos B)=b^(2)-c^(2)

In DeltaABC , prove that: a(bcosC-(c)cosB)=b^(2)-c^(2)

In any DeltaABC , prove that a(bcosC-c cosB)=(b^(2)-c^(2))

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

In DeltaABC , prove that: a(cosC-cosB)=2(b-c)cos^(2)A/2

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

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

In any Delta ABC, prove that: (sin B)/(sin C)=(c-a cos B)/(b-a cos C)

In any Delta ABC ,prove that (sin B)/(sin C)=(c-a cos B)/(b-a cos C)

In any Delta ABC, prove that :a cos A+b cos B+c cos C=2a sin B sin C

RD SHARMA-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-Solved Examples And Exercises
  1. The upper part of a tree broken over by the wind makes an angle of 30^...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Two ships leave port at the same time. One goes 24 km per hour in the ...

    Text Solution

    |

  10. A lamp post is situated at the middle point M of the side AC of a t...

    Text Solution

    |

  11. Two trees, A and B are on the same side of a river. From a point C in ...

    Text Solution

    |

  12. In a A B C , prove the following : In a DeltaA B C ,\ if\ a=5, m\ b=...

    Text Solution

    |

  13. In a DeltaA B C , prove the following :\ If\ a=sqrt(2),\ b=sqrt(3)\ a...

    Text Solution

    |

  14. In a DeltaA B C , prove the following : The sides of a triangle area ...

    Text Solution

    |

  15. In a Delta A B C , prove the following :If a=18 ,\ b=24 ,\ c=30 , fin...

    Text Solution

    |

  16. In a DeltaA B C , prove the following : c\ (acosB-bcosA)=a^2-b^2dot

    Text Solution

    |

  17. In a DeltaA B C , prove the following : (c^2+b^2-a^2)tanA=(a^2+c^2-b^...

    Text Solution

    |

  18. In a Delta A B C , prove the following : (c-b\ cos A)/(b-c\ cos A)=(c...

    Text Solution

    |

  19. In a Delta A B C , prove the following : \ a(cos B+cos C-1)+b(cos C+c...

    Text Solution

    |

  20. In a DeltaA B C , prove the following : a\ cos A+b\ cos B+c cos C=2as...

    Text Solution

    |