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

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

Text Solution

Verified by Experts

`R.H.S. = (b^2+c^2-a^2)/(4cotA)`
` = (b^2+c^2-a^2)/(4cosA/sinA)`
` = (b^2+c^2-a^2)sinA/(4cosA)`
`=1/4(b^2+c^2-a^2)sinA/((b^2+c^2-a^2)/(2bc))`
`= 1/4*2bc*sinA`
`=1/2bcsinA = Delta(`Area of `Delta ABC).`
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

In any DeltaABC , prove that Delta=(b^(2)+c^(2)-a^(2))/(4cotA) .

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

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

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

In any triangle A B C prove that: sin((B-C)/2)=((b-c)/a)cosA/2

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

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

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

For any triangle ABC, prove that (b^2 - c^2) cotA + (c^2 - a^2) cotB + (a^2 - b^2) cotC = 0

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

RD SHARMA ENGLISH-SINE AND COSINE FORMULAE AND THEIR APPLICATIONS-All Questions
  1. In a Delta A B C , ifsinAa n dsinB are the roots of the equation c^2...

    Text Solution

    |

  2. In any A B C , prove that: Delta=(a^2-b^2)/2dot(sinAsinB)/(sin(A-B))

    Text Solution

    |

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

    Text Solution

    |

  4. In a triangle A B C ,a=4,b=3,/A=60^0 then c is root of the equation c^...

    Text Solution

    |

  5. In any A B C ,2(bc cosA+ ca cosB+ab cosC) =

    Text Solution

    |

  6. In any A B C , the value of 2a csin((A-B+C)/2) is (a)a^2+b^2-c^2 ...

    Text Solution

    |

  7. In a A B C , if (c+a+b)(a+b-c)=a b , then the measure of angel C is p...

    Text Solution

    |

  8. If any triangle A B C , that: (b^2-c^2)/(cosB+cosC)+(c^2-a^2)/(cosC+co...

    Text Solution

    |

  9. In a right angled triangle ABC, write the value of sin^2 A + sin^2 B+ ...

    Text Solution

    |

  10. Prove that, (asin(B-C))/(b^(2)-c^(2)) = (bsin(C-A))/(c^(2)-a^(2)) = ...

    Text Solution

    |

  11. In a A B C , if cosC=(sinA)/(2sinB) , prove that the triangle is isos...

    Text Solution

    |

  12. Problem on sine rule Type:-2 (i)The angle of elevation of the top of t...

    Text Solution

    |

  13. (sqrt(sinA)-sqrt(sinB))/(sqrt(sinA)+sqrt(sinB)) = (a+b-2sqrt(ab))/(a-b...

    Text Solution

    |

  14. Let O be a point inside a triangle A B C such that /O A B=/O B C=/O C ...

    Text Solution

    |

  15. The angle of elevation of the top of a tower from a point A due south ...

    Text Solution

    |

  16. (bsecB+csecC)/(tanB+t a n C)=(csecC+asecA)/(tanC+t a n A)=(asecA+bsecB...

    Text Solution

    |

  17. a(cosC-cosB)=2(b-c)cos^2A/2

    Text Solution

    |

  18. a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0 .

    Text Solution

    |

  19. cos(2A)/a^2-cos(2B)/b^2 = 1/a^2-1/b^2

    Text Solution

    |

  20. In a Delta A B C ,\ if\ a=2,\ b=3\ a n d\ sin A=2/3 then find /B

    Text Solution

    |