Home
Class 12
MATHS
Prove that acosA+bcosB+ccosClt=sdot...

Prove that `acosA+bcosB+ccosClt=sdot`

Text Solution

Verified by Experts

`a cos a + b cos B + c cos C`
`= R(2 sin A cos A + 2 sin B cos B + 2 sin C cos C)`
`=R (sin 2A + sin 2B + sin 2C)`
`=4R sin A sin B sin C`
`=(2)/(R) (2R^(2) sin A sin B sin C)`
`= (2)/(R) Delta`
`=2(rs)/(R) le s " " [:' R ge 2r]`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Concept application exercise 5.2|8 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

For any triangle ABC prove that acosA+bcosB +c cosC=2a sinBsinC

Prove that ln(1+x) 0.

Prove that, log_(2)2=1

Prove that cos(60^(@)+A) + cos(60^(@)-A)-cosA=0

Prove that, log_(5)25=2

In a triangle ABC, (acosA+bcosB+ccc cosC)/(a+b+c) is equal to

Prove that acetylene is an unsaturated hydrocarbon.

Prove that a cyclic rhombus is a square

Use logical method to prove the following : For any two sets A and B prove that A subseteq B iff B' subseteq A'

Prove that an isosceled trapeqium is a cyclic quqdrilatral.

CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. Given a right triangle with /A =90^@. Let M be the mid-point of BC. If...

    Text Solution

    |

  2. Prove that the distance between the circumcenter and the incenter of ...

    Text Solution

    |

  3. Prove that acosA+bcosB+ccosClt=sdot

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. If in A B C , the distances of the vertices from the orthocentre are ...

    Text Solution

    |

  6. ABC is an acute angled triangle with circumcenter O and orthocentre H....

    Text Solution

    |

  7. In a acute angled triangle ABC, proint D, E and F are the feet of the ...

    Text Solution

    |

  8. Prove that he distance between the circum-centre and the ortho-centre ...

    Text Solution

    |

  9. Let ABC be an acute angled triangle whose orthocentre is at H. If a...

    Text Solution

    |

  10. In A B C , let L ,M ,N be the feet of the altitudes. The prove that s...

    Text Solution

    |

  11. The lengths of the medians through acute angles of a right-angled tr...

    Text Solution

    |

  12. Two medians drawn from the acute angles of a right angled triangle ...

    Text Solution

    |

  13. Prove that r1+r2+r3-r=4R

    Text Solution

    |

  14. If r1 =r2+r3+r, prove that the triangle is right angled.

    Text Solution

    |

  15. Prove that (r(1+r2))/1=2R

    Text Solution

    |

  16. Prove that (r+r1)tan((B-C)/2)+(r+r2)tan((C-A)/2)+(r+r3)tan((A-B)/2)=0

    Text Solution

    |

  17. If the distance between incenter and one of the excenter of an equi...

    Text Solution

    |

  18. If I1, I2, I3 are the centers of escribed circles of triangle A B C ,...

    Text Solution

    |

  19. Prove that the sum of the radii of the circles, which are, respectiv...

    Text Solution

    |

  20. If the area of the circle is A1 and the area of the regular pentagon i...

    Text Solution

    |