Home
Class 12
MATHS
In triangle ABC , prove that (b+c)cos A ...

In `triangle ABC` , prove that `(b+c)cos A +(c+a)cos B +(a+b)cos C=a+b+c`.

A

`0`

B

`1`

C

`a+b+c`

D

`2(a+b+c)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 2 (LEVEL I)|25 Videos

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 2 (LEVEL II)|6 Videos

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -II Previous Year /JEE Advanced|22 Videos

  • STRAIGHT LINE

    MOTION|Exercise Exercise 4 Lelvel -II|7 Videos

Similar Questions

Explore conceptually related problems

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

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

In triangle ABC , prove that (1) a=b cos C+c cos B (2) b=a cos C+c cos A .

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

For any triangle ABC,prove that a cos A+b cos B+c cos C=2a sin B sin C

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

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

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

In triangle ABC, prove that (b/c+c/b) cosA +(a/b+b/a) cos C+(a/c+c/a)cosB=3

In any triangle,prove that b cos B+c cos C=a cos(B-C)

MOTION-SOLUTION OF TRIANGLE-EXERCISE -1
  1. The distance between the middle point of BC and the foot of the perpen...

    Text Solution

    |

  2. In DeltaABC, if AB=5cm, BC=13cm and CA=12cm, then the distance to vert...

    Text Solution

    |

  3. In triangle ABC , prove that (b+c)cos A +(c+a)cos B +(a+b)cos C=a+b+c.

    Text Solution

    |

  4. (b-c)/acos^2 (A/2)+(c-a)/bcos^2(B/2)+(a-b)/c cos^2(C/2)=

    Text Solution

    |

  5. Prove that bc cos^(2).(A)/(2) + ca cos^(2).(B)/(2) + ab cos^(2).(C)/(2...

    Text Solution

    |

  6. In a triangleABC, [tan(A/2) tan(C/2)] is equal to

    Text Solution

    |

  7. In A B C , the median A D divides /B A C such that /B A D :/C A D=2:1...

    Text Solution

    |

  8. If the median AD of triangle ABC makes an angle pi/4 with the side BC,...

    Text Solution

    |

  9. In a DeltaABC, A=(2pi)/3, b-c=3sqrt3 cm and area(DeltaABC)=(9sqrt3)/2 ...

    Text Solution

    |

  10. If the area of triangleABC is triangle =a^(2) -(b-c)^(2), then: tanA =

    Text Solution

    |

  11. If the sides of a triangles are 3:7:8, then ratio R:r

    Text Solution

    |

  12. In a right angled triangle R is equal to

    Text Solution

    |

  13. In a triangle a = 13 , b = 14, c = 15, r =

    Text Solution

    |

  14. In an equilateral triangle, the inradius and the circumradius are conn...

    Text Solution

    |

  15. In a triangle ABC, right angled at B, then

    Text Solution

    |

  16. If the area of triangles is 100 sq. cm, r1= 10 cm and r2= 50 cm, then...

    Text Solution

    |

  17. In a triangleABC, the inradius and three exradii are r,r1,r2" and "r3 ...

    Text Solution

    |

  18. In a triangleABC if r1 lt r2 lt r3, then

    Text Solution

    |

  19. In a triangle ABC, if (a-b)/(b-c)= (s-a)/(s-c), then r1,r2,r3 are in

    Text Solution

    |

  20. If AD, BE and CF are the medians of a ABC ,then (AD^(2)+BE^(2)+CF^(2))...

    Text Solution

    |