Home
Class 12
MATHS
If A,B,C are the angles off DeltaABC, th...

If A,B,C are the angles off `DeltaABC`, then `cotA*cotB+cotB*cotC+cotC*cotA`=

A

0

B

1

C

2

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Given,
`A+B+C=pi`
`rArrA+B+pi-C`
`rArrcot(A+B)=cot(pi-C)`
`rArr(cotAcotB-1)/(cotA+cotB)=-cotC`
`rArrcotAcotB-1=-cotAcotC-cotBcotC`
`rArrcotAcotB+cotBcotC+cotCcotA=1`
Promotional Banner

Topper's Solved these Questions

  • MHTCET 2017

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHMATICS|50 Videos

  • MHTCET 2019 PAPER 1

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

In a triangle A+B+C=90 then prove that cotA+cotB+cotC=cotAcotBcotC

Statement-1 : If angles A, B, C of DeltaABC are acute, then cotA cotB cotCle(1)/(3sqrt(3)). Statement-2: If a, b, c are positive real numbers and -ltmlt1 , then (a^(m)+b^(m)+c^(m))/(3)lt((a+b+c)/(3))^(m)

If A+B+C=pi , prove that: cotB cotC + cotC cotA +cotA + cotA cotB=1 .

If A+B+C=pi/2 , show that : cotA+cotB+cotC=cotA cotB cotC

If A+B+C=pi , show that : tanA+tanB+tanC=tanA.tanB.tanC Hence. Deduce the value of : cotA.cotB+cotB.tanC+cotC.cotA

If A+B+C=pi and A, B, C are acute positive angles and cotA cotB cotC = k, then

If a^(2),b^(2) and c^(2) are in AP, then cotA, cotB and cotC are in

If A, B, C, D be the angles of a quadrilateral, prove that : (tanA+tanB+tanC+tanD)/(cotA+cotB+cotC+cotD) = tan A tan B tan C tan D

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MHTCET 2018-Mathematics
  1. Letters in the word HULULULU are rearranged. The probability of all th...

    Text Solution

    |

  2. The sum of the first 10 terms of the series 9+99+999+ . . . Is

    Text Solution

    |

  3. If A,B,C are the angles off DeltaABC, then cotA*cotB+cotB*cotC+cotC*co...

    Text Solution

    |

  4. if int(dx)/(sqrt(16-9x^(2)))=Asin^(-1)(Bx)+C, then A+B=

    Text Solution

    |

  5. Evaluate: inte^x\ ((2+sin2x)/(1+cos2x))\ dx

    Text Solution

    |

  6. A coin is tossed three times. If X denotes the absolute difference bet...

    Text Solution

    |

  7. If 2 sin(theta+(pi)/(3))=cos(theta-(pi)/(6)), then tantheta=

    Text Solution

    |

  8. The area of the region bounded by x^(2)=4y,y=1,y=4 and the Y-axis lyin...

    Text Solution

    |

  9. if f(x)=(e^(x^(2))-cosx)/(x^(2)), for xne0 is continuous at x=0, then ...

    Text Solution

    |

  10. The maximum value of 2x+y subject to 3x+5yle26and5x+3yle30,xge0,yge0...

    Text Solution

    |

  11. If vec(a),vec(b),vec(c) are mutually perpendicular vectors having magn...

    Text Solution

    |

  12. If points P(4,5,x),Q(3,y,4) and R(5,8,0) are collinear, then the value...

    Text Solution

    |

  13. If the slope of one of the lines given by ax^(2)+2hxy+by^(2)=0 is two ...

    Text Solution

    |

  14. The equation of the line passing through the point (-3,1) and bisectin...

    Text Solution

    |

  15. The negation of the statement: ''Getting above 95% marks is necessary ...

    Text Solution

    |

  16. cos1^@ . cos2^@ . cos3^@.........cos179^@ is equal to :

    Text Solution

    |

  17. If the planes x-c y-b z=0,c x=y+a z=0a n db x+a y-z=0 pass through a s...

    Text Solution

    |

  18. The lines represented by the equation x^2-y^2-x+3y-2=0 are

    Text Solution

    |

  19. A die is rolled. If X denotes the number of positive divisors of the o...

    Text Solution

    |

  20. A die is thrown four times. The probality of getting perfect square in...

    Text Solution

    |