Home
Class 12
MATHS
If A, B, C, D be the angles of a quadril...

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`

A

tan A tan B tan C tan D

B

cot A cot B cot C cot D

C

`tan^(2)A + tan^(2)B + tan^(2)C + tan^(2)D`

D

`sum tan A tan B tanC`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos
  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

If A,B,C,D are the angles of a quadrilateral, then (tan A+tan B+tan C+tan D)/(cot A+cot B+cot C+cot D) is equal to: (a) tan A tan B tan C tan D(b)tan^(2)A+tan^(2)B+tan^(2)C+tan^(2)D(d)sum tan A tan B tan C

If A,B,C,D are the angles of quadrilateral, then find (sum tan A)/(sum cot A).

If A,B,C,D are the four angles taken in order of a cyclic quadrilateral prove that tan A+tan B+tan C+tan D=0

If A+C=B , then tan A tan B tan C = ?

(a) tan A+tan B+tan C=tan A tan B tan C

If A+B+C=pi , prove that : (tanA+tanB+tanC) (cotA+cotB+cotC)=1+secA secB secC .

If,A,B,C are angles of a triangle and if none of them is equal to (pi)/(2) ,then tan A+tan B+tan C is cot A cotB cot C tan A tan B tan C sin A sin B sin C cos A cos B cos C

(tan A+tan B-tan C+tan A tan B tan C)/(1-tan A tan B+tan B tan C+tan C tan A)

If A+B+C= pi , prove that tan A+tan B+tan C= tanA tan B tan C

RESONANCE-DPP-QUESTION
  1. The minimum value of the expression |x-p+|x-15|+|x-p-15| for ' x ' in ...

    Text Solution

    |

  2. If the graph of the function y = f(x) is as shown : The graph of ...

    Text Solution

    |

  3. If A, B, C, D be the angles of a quadrilateral, prove that : (tanA+tan...

    Text Solution

    |

  4. If the sum of n term of the series (5)/(1.2.3) + (6)/(2.3.4) + ( 7)/(3...

    Text Solution

    |

  5. If the 8th term of an A.P. is 31 and the 15th term is 16 more than ...

    Text Solution

    |

  6. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

    Text Solution

    |

  7. Let f(r) = sum(j=2)^(2008) (1)/(j^(r)) = (1)/(2^(r))+(1)/(3^(r))+"…."+...

    Text Solution

    |

  8. If sinalphacosbeta = (-1)/(2), then find the range of value of cosalph...

    Text Solution

    |

  9. -cos(A+B)cos(B-A) =

    Text Solution

    |

  10. Find the value of xsqrt(6x^(4) + 4x^(2) + 2) gt -2x^(2) + 5x - 4

    Text Solution

    |

  11. S = n xx 10^(6m) + n xx 10^(6m - 1) + n xx 10^(6m-2)+ "…." + nxx 10 + ...

    Text Solution

    |

  12. Number of roots of (x^(2)+5x+7)(-x^(2)+3x-4) = 0

    Text Solution

    |

  13. If the roots of Quadratic i^(2)x^(2)+5ix-6 are a+ib and c +id (a,b,c,d...

    Text Solution

    |

  14. S(10) = cos'(pi)/(180) + cos'(3pi)/(180) + "….." cos '(19pi)/(180)

    Text Solution

    |

  15. Find the sum of the series 31^(3) + 32^(3) + "……." 50^(3)

    Text Solution

    |

  16. Find maximum value of a^(2)b^(3) if a+b=2. When a & b are positive num...

    Text Solution

    |

  17. Find the roots of the equation x^(2) + ix - 1 - i = 0

    Text Solution

    |

  18. solve ||x-2|-1|lt 2

    Text Solution

    |

  19. If x^(3) + 2x-3 = 0 then then number of real values of 'x' satisfying ...

    Text Solution

    |

  20. solve for x |x+1| + |x-2| + |x-5| = 4

    Text Solution

    |