Home
Class 11
MATHS
If for a triangle ABC , cot A+cotB+cotC=...

If for a triangle ABC , cot A+cotB+cotC=`sqrt3`,then show that the triangle is equilateral.

Promotional Banner

Topper's Solved these Questions

  • ANNUAL EXAMINATION QUESTION PAPERS 2016

    UNITED BOOK HOUSE|Exercise EXERCISE|51 Videos

  • ANNUAL EXAMINATION QUESTION PAPERS 2018

    UNITED BOOK HOUSE|Exercise EXERCISE|53 Videos

Similar Questions

Explore conceptually related problems

If in any triangle ABC, cot A + cotB + cotC = sqrt(3) , prove that, the triangle is equilateral.

In triangle ABC if cotA +cot B +cot C=sqrt3 then prove that the triangle is an equilateral triangle

In any triangle ABC, if cosA + cos B + cosC =3/2 , then show that the triangle is equilateral.

If in triangle ABC cosA+cosB+cosC=3/2 then prove that triangle is equilateral

In the triangle ABC, if cos 3 A + cos 3B+ cos 3C=1 , show that the triangle is obtuse-angled.

If in a triangle ABC, a=3, b=5 and c=7, show that the triangle is obtuse angled.

In any triangle ABC, if sin^(2)A + sin^(2)B + sin^(2)C = 9/4 , show that the triangle is equilateral.

In /_\ABC .if cos A=(sinB)/(sinC) ,then show that the triangle is right angles triangle.

If the co-ordinate of three vertices of a- triangle are (9, 1, -3), (1.- 1, -5) and (3, 1, 3). Show that the triangle is equilateral

In the triangle ABC, If "cosec"^(2) A + " cosec "^(2)B + " cosec "^(2) C=4 , show that the triangle is equilateral.

UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2017-EXERCISE
  1. For any three sets A,B and C ,prove that A-(BcupC)=(A-B)cap(A-C).

    Text Solution

    |

  2. If sin^4alpha/a+cos^4alpha/b=1/(a+b),then show that sin^8alpha/a^3+cos...

    Text Solution

    |

  3. If for a triangle ABC , cot A+cotB+cotC=sqrt3,then show that the trian...

    Text Solution

    |

  4. If n in N,then prove by mathematical induction that 7^(2n)+2^3(n-1).3^...

    Text Solution

    |

  5. If z=x+iy and (z-i)/(z+1)is purely imaginary,then show that the point ...

    Text Solution

    |

  6. How many odd numbers of fve digits can be formed with the digits 3,6,7...

    Text Solution

    |

  7. Prove that the middle term in the expansion of (1+x)^(2n)is(1.3.5........

    Text Solution

    |

  8. If the ratio the sum of 1st n terms of two arithemtic series is (4n-13...

    Text Solution

    |

  9. Find the equations of the lines passing thorugh the point (4,5)making ...

    Text Solution

    |

  10. If the equation of the side BC of an equilateral triangle ABC is x+y=2...

    Text Solution

    |

  11. A circle in the first quadrant touches both the axes its centre lies o...

    Text Solution

    |

  12. Evaluate:underset(x rarr 0)(lim)((e^(x)-1)log(1+x))/(sin^(2)x)

    Text Solution

    |

  13. Find from the first principle,the derivative of f(x)=sec2xat x=pi/8.

    Text Solution

    |

  14. Prove by method of contradiction that sqrt5is an irrational number

    Text Solution

    |

  15. Prove that truth table ~(pvq)=~p~q.

    Text Solution

    |

  16. If 30 dates are named at random,find the probability that 5 of them wi...

    Text Solution

    |

  17. calculate the mean deviation about median for the following data:

    Text Solution

    |

  18. Solve: 4 sin x sin 2x sin 4x =sin3x.

    Text Solution

    |

  19. if tan (theta/2)=sqrt((1-e)/(1+e))tan (varphi/2),then prove that cos v...

    Text Solution

    |

  20. Solve the following inequation (|x+2|+2x)/(x+2)>2.

    Text Solution

    |