Home
Class 11
MATHS
With usual notations, if in a triangle A...

With usual notations, if in a triangle `A B C(b+c)/(11)=(c+a)/(12)=(a+b)/(13)` , then prove that: `(cosA)/7=(cosB)/(19)=(cosC)/(25)`

Text Solution

AI Generated Solution

To solve the problem, we need to show that if \((b+c)/11 = (c+a)/12 = (a+b)/13\), then \((\cos A)/7 = (\cos B)/19 = (\cos C)/25\). ### Step-by-Step Solution: 1. **Let the common ratio be \(K\)**: \[ \frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13} = K \] ...
Promotional Banner

Topper's Solved these Questions

  • SETS

    RD SHARMA ENGLISH|Exercise All Questions|228 Videos

  • SOME SPECIAL SERIES

    RD SHARMA ENGLISH|Exercise All Questions|69 Videos

Similar Questions

Explore conceptually related problems

With usual notion, if in triangle A B C , (b+c)/(11)=(c+a)/(12)=(a+b)/(13),t h e np rov et h a t (cosA)/7=(cosB)/(19)=(cosC)/(25)

In a triangle ABC , if (b+c)/(11)=(c+a)/(12)=(a+b)/(13) , then cos A=

With usual notations, if in a triangle ABC (b+c)/(11) = (c+a)/(12) = (a+b)/(13) , then cos A : cos B : cos C is :

In any DeltaA B C ,(b+c)/(12)=(c+a)/(13)=(a+b)/(15),\ then prove that (cos A)/2=(cos B)/7=(cos C)/(11)dot

If in a triangle ABC , (b+c)/11=(c+a)/12=(a+b)/13 then cosA is equal to

Prove that : (a b c)/scosA/2cosB/2cosC/2=

If in a triangle ABC, (cosA)/a=(cosB)/b=(cosC)/c ,then the triangle is

In DeltaABC , prove that: (c-bcosA)/(b-c (cosA))=(cosB)/(cosC)

Prove that (b+c)cosA+(c+a)cosB+(a+b)cosC=2sdot

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

RD SHARMA ENGLISH-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-All Questions
  1. Two boats leave a place at the same time. One travels 56 km in the dir...

    Text Solution

    |

  2. In any triangle A B C , prove that: a^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B...

    Text Solution

    |

  3. With usual notations, if in a triangle A B C(b+c)/(11)=(c+a)/(12)=(a+b...

    Text Solution

    |

  4. If a^2,b^2,c^2 are in A.P., prove that cotA ,cotB ,cotC are in AdotPdo...

    Text Solution

    |

  5. If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the ...

    Text Solution

    |

  6. In a triangle A B C ,/C=60^0, then prove that: 1/(a+c)+1/(b+c)=3/(a+b+...

    Text Solution

    |

  7. Prove that b(c cosA-acosC)=c^2-a^2

    Text Solution

    |

  8. 2(bc cosA+c acosB+a bcosC)=a^2+b^2+c^2

    Text Solution

    |

  9. In a A B C , if /B=60^0 , prove that (a+b+c)(a-b+c)=3c a

    Text Solution

    |

  10. In any DeltaABC , prove that: (sinB)/(sinC)=(c-acosB)/(b-acosC)

    Text Solution

    |

  11. In any A B C , prove that: 2{asin^2C/2+csin^2A/2}=a+c-b

    Text Solution

    |

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

    Text Solution

    |

  13. In any A B C , prove that: (b+c)cos A+(c+a)cos B+(a+b)cos C=a+b+c

    Text Solution

    |

  14. For any triangle ABC, prove that a(bcosC-c cosB)=b^2-c^2

    Text Solution

    |

  15. In a Delta A B C ,if a=2,/B=60^0a n d/C=75^0 , then b= (a)sqrt(3) ...

    Text Solution

    |

  16. If a^2,b^2,c^2 are in A.P., prove that cotA ,cotB ,cotC are in AdotPdo...

    Text Solution

    |

  17. In any triangle A B C , prove that: (1+cos(A-B)cos C)/(1+cos(A-C)cos B...

    Text Solution

    |

  18. In any triangle. if(a^2-b^2)/(a^2+b^2)=("sin"(A-B))/("sin"(A+B)) , the...

    Text Solution

    |

  19. For any triangle ABC, prove that acosA+bcosB+ccosC=2asinBsinC

    Text Solution

    |

  20. In any triangle A B C , prove that: (b-c)cot (A/2)+(c-a)cot (B/2)+(a-b...

    Text Solution

    |