Home
Class 12
MATHS
If a(1),a(2),a(3),….a(n) is a.p with com...

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

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

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|72 Videos

  • INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

  • LIMITS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 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) 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) are in arithmetic progression with common difference d, then evaluate the following expression: tan{tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a^(2)a_(3)))+tan^(-1)((d)/(1+a_(3)a_(4)))+...+tan^(-1)((d)/(1+a_(n-1)a_(n)))}

If a_(0),a_(1),a_(3),a_(4)......... are in AP with common difference d where d!=0,1,-1, then the det[[a_(1)a_(2),a_(1),a_(0)a_(2)a_(3),a_(2),a_(1)a_(3)a_(4),a_(3),a_(2)]] is

If a_(1),a_(2),a_(3),...,a_(2n+1) are in A.P.then (a_(2n+1)-a_(1))/(a_(2n+1)+a_(1))+(a_(2n)-a_(2))/(a_(2n)+a_(2))+...+(a_(n+2)-a_(n))/(a_(n+2)+a_(n)) is equal to (n(n+1))/(2)xx(a_(2)-a_(1))/(a_(n+1)) b.(n(n+1))/(2) c.(n+1)(a_(2)-a_(1)) d.none of these

OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
  1. The value of (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec...

    Text Solution

    |

  2. If a,b are positive quantitis and if a(1)=(a+b)/(2), b(1)=sqrt(a(1)b) ...

    Text Solution

    |

  3. tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equ...

    Text Solution

    |

  4. If a(1),a(2),a(3),….a(n) is a.p with common difference d then tan{tan...

    Text Solution

    |

  5. If x=sin(2tan^(- 1)2), y=sin(1/2tan^(- 1)(4/3)) , then -

    Text Solution

    |

  6. Which of the following angles is greater? theta1=sin^(-1)(4/5)+sin^(-...

    Text Solution

    |

  7. The value of cos[1/2 cos^(-1){cos(sin^(-1)((sqrt63)/(8)))}] is

    Text Solution

    |

  8. Solve tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1)"\ "8/(31)

    Text Solution

    |

  9. If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)...

    Text Solution

    |

  10. The sum of the two angles cot^(-1) 3 and cosec^(-1) sqrt(5) is

    Text Solution

    |

  11. Show that: cos(2tan^(-1)1/7)=sin(4^(-1)1/3)

    Text Solution

    |

  12. Number of integral solutions of the equation 2 sin^-1sqrt(x^2-x +1 )+ ...

    Text Solution

    |

  13. cos{cos^(-1)(-1/7)+sin^(-1)(-1/7)} =

    Text Solution

    |

  14. If cos^(-1)x + cos^(-1)y + cos^(-1)z = 3pi, then xy + yz +zx is equal ...

    Text Solution

    |

  15. sin[1/2cos^(- 1)4/5]

    Text Solution

    |

  16. lf x >=0 and theta = sin^(-1)x + cos^(-1)x-tan^(-1) x, then

    Text Solution

    |

  17. If tan^(-1)a+tan^(-1)b+tan^(-1)c=pi then prove tjhat a+b+c=abc

    Text Solution

    |

  18. The value of cot(c o s e c^(- 1)5/3+tan^(- 1)(2/3))i s

    Text Solution

    |

  19. Prove the following : sin^(-1)4/5+2\ tan^(-1)1/3=pi/2

    Text Solution

    |

  20. The equation sin^-1x-cos^-1x=cos^-1(sqrt3/2) has

    Text Solution

    |