Home
Class 12
MATHS
In DeltaABC, " if " b^(2) + c^(2) = 2a^(...

In `DeltaABC, " if " b^(2) + c^(2) = 2a^(2)`, then value of `(cotA)/(cot B + cot C)` is

A

`(1)/(2)`

B

`(3)/(2)`

C

`(5)/(2)`

D

`(5)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(cotA)/(cotB cotC) = ((R(b^(2) + c^(2) -a^(2)))/(abc))/((R(a^(2) + c^(2) -b^(2)))/(abc) + (R(a^(2) + b^(2) -c^(2)))/(abc))`
`= (b^(2) + c^(2) -a^(2))/(2a^(2))`
`= (2a^(2) -a^(2))/(2a^(2))`
`= (1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Multiple)|24 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise (Comprehension)|34 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.11|4 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|32 Videos

Similar Questions

Explore conceptually related problems

In a Delta ABC if 9(a^(2)+b^(2))=17c^(2) then the value of the (cot A+cot B)/(cot C) is

If, in a Delta ABC, b^(2) + c^(2) = 3a^(2) , then : cot B + cot C - cot A =

In a triangle ABC if a^(2)+b^(2)=101c^(2) then find the value of (cot C)/(cot A+cot B)

In /_\ABC ,if a^(2)+b^(2)=3c^(2) ,then find the value of cot A+cot B-cot C?

In a /_ABC, if b^(2)+c^(2)=3a^(2), then cot B+cot C-cot A is equal to

In Delta ABC,a^(2)+c^(2)=2002b^(2) then (cot A+cot C)/(cot B) is equal to

In Delta ABCa^(2)+b^(2)=2019c^(2), then 1009((cot A+cot B)/(cot C)) is

In a DeltaABC , 2A(cot B + cot C)=

In DeltaABC , if (sinA)/(3)=(cosB)/(3)=(tanC)/(2) , then the value of ((sinA)/(cot2A)+(cosB)/(cot2B)+(tan C)/(cot 2 C)) is

CENGAGE-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercise (Single)
  1. In any triangle ABC, (a^(2) + b^(2) + c^(2))/(R^(2)) has the maximum v...

    Text Solution

    |

  2. In triangle ABC, R (b + c) = a sqrt(bc), where R is the circumradius o...

    Text Solution

    |

  3. In DeltaABC, " if " b^(2) + c^(2) = 2a^(2), then value of (cotA)/(cot ...

    Text Solution

    |

  4. If sin theta and -cos theta are the roots of the equation ax^(2) - bx ...

    Text Solution

    |

  5. If D is the mid-point of the side B C of triangle A B C and A D is per...

    Text Solution

    |

  6. In a triangle ABC, if cotA :cotB :cotC = 30: 19 : 6 then the sides a, ...

    Text Solution

    |

  7. In Delta ABC, P is an interior point such that angle PAB = 10^(@), ang...

    Text Solution

    |

  8. In DeltaABC, if AB = c is fixed, and cos A + cosB + 2 cos C = 2 then t...

    Text Solution

    |

  9. If in A B C ,A=pi/7,B=(2pi)/7,C=(4pi)/7 then a^2+b^2+c^2 must be R^2 ...

    Text Solution

    |

  10. In Delta ABC, "cot"(A)/(2) + "cot" (B)/(2) + "cot" (C)/(2) is equal to

    Text Solution

    |

  11. In Delta ABC, (cot. (A)/(2) + cot. (B)/(2)) (a sin.^(2) (B)/(2) + b si...

    Text Solution

    |

  12. In a right-angled isosceles triangle, the ratio of the circumradius an...

    Text Solution

    |

  13. In the given figure, what is the radius of the inscribed semicircle ha...

    Text Solution

    |

  14. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

    Text Solution

    |

  15. In triangle ABC, let angle C = pi//2. If r is the inradius and R is ci...

    Text Solution

    |

  16. In the given figure, AB is the diameter of the circle, centered at O. ...

    Text Solution

    |

  17. In triangle ABC, if P, Q, R divides sides BC, AC, and AB, respectively...

    Text Solution

    |

  18. If the angles of a traingle are 30^(@) and 45^(@) and the included sid...

    Text Solution

    |

  19. In triangle A B C , base B C and area of triangle are fixed. The locus...

    Text Solution

    |

  20. Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1...

    Text Solution

    |