Home
Class 12
MATHS
If sum(r=1)^(infty) tan ^(-1)((1)/(2 r^(...

If `sum_(r=1)^(infty) tan ^(-1)((1)/(2 r^(2)))=t` then `tan t` is equal to

A

`(2)/(3)`

B

1

C

`(sqrt(5))/(3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRAL

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|404 Videos
  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|354 Videos

Similar Questions

Explore conceptually related problems

If tan A=(1)/(2), tan B=(1)/(3) then tan (2 A+B) is equal to

sum_(r=1)^(n)(sum_(p=0)^(r-1)""^(n)C_(r)""^(r)C_(p)2^(p)) is equal to:

if sinx =(2t)/(1+t^(2)) , tany= (2t)/(1- t^(2)) then (dy)/(dx) is equal to

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to

The value of fe^(x)(x^(2)tan^(-1) x + tan^(-1) x + 1)/(x^(2) + 1) dx is equal to

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) where T_(r) denotes the rth term of the series. Find lim_(nto oo) sum_(r=1)^(n)(1)/(T_(r)) .

The value of tan (2 tan^(-1). (1)/(5) - (pi)/(4) ) is equal to

The value of tan[2" tan"^(-1)(1)/(5)-(pi)/(4)] is equal to

age0 , then sum_(n=1)^(infty)((a)/(a+1))^(n) equals

(1+tan^(2)60^(@))^(2) is equal to:

HIMALAYA PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. The number of real solutions of the equation tan^(-1) sqrt( x ( x + 1)...

    Text Solution

    |

  2. If tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x,xgt0 find x

    Text Solution

    |

  3. If sum(r=1)^(infty) tan ^(-1)((1)/(2 r^(2)))=t then tan t is equal to

    Text Solution

    |

  4. If sin^(-1) ((2a)/(1+a^2))+cos^(-1) ((1-a^2)/(1+a^2))=tan^(-1) ((2x)/(...

    Text Solution

    |

  5. The solution set of the equation sin ^(-1) x=2 tan ^(-1) x is

    Text Solution

    |

  6. Let (x, y) be such that sin ^(-1)(alpha x)+cos ^(-1) y+cos ^(-1)(b x y...

    Text Solution

    |

  7. Let cos (2 tan ^(-1) x)=(1)/(2) then the value fo x is

    Text Solution

    |

  8. The value of x where x gt 0 and tan (sec ^(-1)((1)/(x)))=sin (tan ^(-1...

    Text Solution

    |

  9. If sin ^(-1) (3)/(x)+sin ^(-1) (4)/(x)=(pi)/(2) then x=

    Text Solution

    |

  10. If tan ^(-1) ((a)/(x))+tan ^(-1) ((b)/(x))=(pi)/(2), then x=

    Text Solution

    |

  11. sin ^(-1)[cot ((sin ^(-1) sqrt((2-sqrt(3))/(4)))+cos ^(-1) (sqrt(12))/...

    Text Solution

    |

  12. The principal value of sin ^(-1)(tan (-(5 pi)/(4))) is

    Text Solution

    |

  13. If sec ^(-1) x=cosec^(-1) y then cos ^(-1) (1)/(x)+cos ^(-1) (1)/(y)=

    Text Solution

    |

  14. sin (2 sin^(-1) sqrt((63)/(65)))=

    Text Solution

    |

  15. cot^(-1)(2.1^(2))+cot^(1)(2.2^(2))+cot^(-1)(2.3)^(2)+………… up to oo =

    Text Solution

    |

  16. If agtbgt0,sec^(-1)((a+b)/(a-b))=2"sin"^(-1)x, then x =

    Text Solution

    |

  17. If tan^(-1)x=(pi)/(4)-tan^(-1)((1)/(3)), then x is

    Text Solution

    |

  18. If x takes negative permissible value, then sin^(-1)x is equal to

    Text Solution

    |

  19. The value of sin [cot^(-1) {cos (tan^(-1)x)}] is :

    Text Solution

    |

  20. If cos ^(-1) x+cos ^(-1) y+cos ^(-1) z=3 pi then x y+y z+z x=

    Text Solution

    |