Home
Class 11
MATHS
If A ,\ B ,\ C are the angles of a trian...

If `A ,\ B ,\ C` are the angles of a triangle, prove that : `cos A+cos B+cos C=1+r/Rdot`

Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ALLEN|Exercise All Questions|1 Videos

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise Do yourself -6|4 Videos

Similar Questions

Explore conceptually related problems

If A,B,C are the angles of a triangal ,prove that : cos A +cos B + cos C = 1+r/R

If A,B,C are angles of a triangle, prove that cosC=-cos(A+B) .

If A , Ba n dC are the angels of a triangle, show that |-1+cos B cos C+cos B cos B cos C+cos A-1+cos A cos A-1+cos B-1+cos A-1|=0

If A , Ba n dC are the angels of a triangle, show that |-1+cos B cos C+cos B cos B cos C+cos A-1+cos A cos A-1+cos B-1+cos A-1|=0

If A ,\ B ,\ C ,\ D are angles of a cyclic quadrilateral, prove that cos A+cos B+cos C+cos D=0.

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

If A, B and C denote the angles of a triangle, then Delta = |(-1,cos C,cos B),(cos C,-1,cos A),(cos B,cos A,-2)| is independent of

If A, B, C are the angles of a right angled triangle, then (cos^2A+ cos^2B+ cos^2C) equals

If A ,B ,C ,D are angles of a cyclic quadrilateral, then prove that cos A+cos B+cos C+cos D=0

If A,B,C,D are the angles of a quadrilateral, prove that "cos"1/2(A+B)+"cos"1/2(C+D)=0 .

ALLEN-SOLUTION AND PROPERTIES OF TRIANGLE-All Questions
  1. The base of a triangle is divided into three equal parts. If t1, t2,t3...

    Text Solution

    |

  2. In a triangle A B C , if a : b : c=4:5:6 , then ratio between its circ...

    Text Solution

    |

  3. If A ,\ B ,\ C are the angles of a triangle, prove that : cos A+cos B+...

    Text Solution

    |

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

    Text Solution

    |

  5. Prove that the distance between the circumcenter and the orthocentre o...

    Text Solution

    |

  6. In the ambiguous case of the solution of triangle, prove that the c...

    Text Solution

    |

  7. If a, b and A are given in a triangle and c(1), c(2) are possible valu...

    Text Solution

    |

  8. If b , c , B are given and b &lt c,prove that cos((A1-A2)/2)=(csinB)/b

    Text Solution

    |

  9. If in a triangle ABC, cos A +cos B+cos C=3/2, prove that the triangle ...

    Text Solution

    |

  10. In a triangle A B C , if cos A+2\ cos B+cos C=2. prove that the sides ...

    Text Solution

    |

  11. In a triangle A B C\ a : b : c=sqrt(3)\ :1\ :\ 1, then the triangle is...

    Text Solution

    |

  12. The sides of a triangle A B C are x , y ,\ sqrt(x^2+y^2+x y) respectiv...

    Text Solution

    |

  13. In a "Delta"A B C\ ((a^2)/(sinA)+(b^2)/(sinB)+(c^2)/(sinC))dotsinA/2si...

    Text Solution

    |

  14. If p1, p2, p3, be the altitudes of a triangle ABC from the vertices A,...

    Text Solution

    |

  15. If in a triangle A B C angle B=90^0 then tan^2(A/2) is (b-c)/a (b) (b-...

    Text Solution

    |

  16. In a triangle A B C ,\ If (a^3+b^3+c^3)/(sin^3A+sin^3B+sin^3C)=343 , ...

    Text Solution

    |

  17. In a Delta ABC if b+c = 3a then cot. (B)/(2). cot. (C )/(2) has the va...

    Text Solution

    |

  18. If a/(sinA)=K , then the area of "Triangle ABC" in terms of K and sine...

    Text Solution

    |

  19. In a triangle A B C ,/c=60^0a n d/A=75^0 . If D is a point on A C such...

    Text Solution

    |

  20. In a ΔABC, a semicircle is inscribed, whose diameter lies on the side ...

    Text Solution

    |