Home
Class 12
MATHS
If a1, a2,a3, ,an is an A.P. with commo...

If `a_1, a_2,a_3, ,a_n` is an A.P. with common difference `d ,` then prove that `"tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+tan^(-1)(d/(11+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)`

A

`(((n-1)d)/(a_(1)+a_(n)))`

B

`(((n-1)d)/(1+a_(1)a_(n)))`

C

`((nd)/(1+a_(1)a_(n)))`

D

`((a_(n)-a_(1))/(a_(n)+a_(1)))`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise Competitive Thinking|218 Videos

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise Evaluation Test|34 Videos

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise Evaluation Test|34 Videos

  • THREE DIMENSIONAL GEOMETRY

    TARGET PUBLICATION|Exercise Evaluation Test|9 Videos

  • VECTORS

    TARGET PUBLICATION|Exercise Evaluation Test|18 Videos

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),a_(n) is an A.P.with common difference d, then prove that tan[tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))+tan^(-1)((d)/(1+a_(n-1)a_(n)))]=((n-1)d)/(1+a_(1)a_(n))

If a_(1), a_(2), a_(3),...., a_(n) is an A.P. with common difference d, then prove that tan[tan^(-1) ((d)/(1 + a_(1) a_(2))) + tan^(-1) ((d)/(1 + a_(2) a_(3))) + ...+ tan^(-1) ((d)/(1 + a_( - 1)a_(n)))] = ((n -1)d)/(1 + a_(1) a_(n))

If a_(1),a_(2),a_(3),….a_(n) is a.p with common difference d then tan{tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3))) +..+ tan^(-1)((d)/(1+a_(n-1)a_(n)))} is equal to

If a_1,a_2,a_3,…………..a_n are in A.P. whose common difference is d, show tht sum_2^ntan^-1 d/(1+a_(n-1)a_n)= tan^-1 ((a_n-a_1)/(1+a_na_n))

If a_1,\ a_2,\ a_3,\ ,\ a_n are in arithmetic progression with common difference d , then evaluate the following expression: tan{tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+tan^(-1)(d/(1+a_3a_4))++tan^(-1)(d/(1+a_(n-1)a_n))}

If a_(1), a_(2), a_(3) are in arithmetic progression and d is the common diference, then tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))=

If a_1,a_2,a_3,...,a_n be in AP whose common difference is d then prove that sum_(i=1)^n a_ia_(i+1)=n{a_1^2+na_1d+(n^2-1)/3 d^2} .

TARGET PUBLICATION-TRIGONOMETRIC FUNCTIONS -Critical Thinking
  1. If (tan^-1x)^2 + (cot^-1x)^2 =(5 pi^2)/8 then x equals :

    Text Solution

    |

  2. cos(tan^(-1)((1)/(3))+tan^(-1)((1)/(2)))=

    Text Solution

    |

  3. cos^-1(4/5)+tan^-1(3/5)=tan^-1(27/11)

    Text Solution

    |

  4. If "tan"^(-1)(x-1)/(x-2)+"tan"^(-1)(x+1)/(x+2)=(pi)/4, find x

    Text Solution

    |

  5. cot^-1[(cot)^(1/2)]+tan^-1[(cotalpha)^(1/2)=x then sin x= (A) 1 (B) co...

    Text Solution

    |

  6. If tan^(-1).(a+x)/(a) + tan ^(-1) ((a-x)/(a)) = (pi)/(6) then prove th...

    Text Solution

    |

  7. Q. the value of tan^-1(a/(b+c))+tan^-1(b/(c+a)), if /=90^@ in triangle...

    Text Solution

    |

  8. सिद्ध कीजिए - tan^(-1).(3)/(4)+tan^(-1).(3)/(5)-tan^(-1).(8)/(19)=(p...

    Text Solution

    |

  9. If x^2 + y^2 + z^2 = r^2 and x, y, z > 0, then tan^-1((xy)/(zr))+tan...

    Text Solution

    |

  10. If cj >0 for i=1,2, , n , prove that tan^(-1)((c1x-y)/(c1y+x))+tan^(-...

    Text Solution

    |

  11. If a1, a2,a3, ,an is an A.P. with common difference d , then prove th...

    Text Solution

    |

  12. tan[2tan^(- 1)(1/5)+pi/4]

    Text Solution

    |

  13. sin[3sin^(-1)((1)/(5))] is equal to

    Text Solution

    |

  14. The value of cot[cos^(-1)(7/25)] is

    Text Solution

    |

  15. If cos(2sin^(-1)x)=1/9, then find the values of xdot

    Text Solution

    |

  16. Find the value of expression: sin(2tan^(-1)1/3)+cos(tan^(-1)2sqrt(2))

    Text Solution

    |

  17. If: tan^(-1)x = sin^(-1)(3/sqrt(10)), then: x=

    Text Solution

    |

  18. If we consider only the principal values then the value inverse trigon...

    Text Solution

    |

  19. sin^(-1)""1/sqrt5+cot^(-1)3=pi/4

    Text Solution

    |

  20. If |(cos(A+B),-sin(A+B),cos2B),(sinA,cosA, sinB),(-cosA, sinA, cosB)|=...

    Text Solution

    |