Home
Class 12
MATHS
The minimum value of n for which tan^(-1...

The minimum value of n for which `tan^(-1)'n/pi gt (pi)/(4), n in N`, is valid is 5.

Text Solution

Verified by Experts

`:' tan^(-1)'(n)/(pi) gt (pi)/(4) rArr n/pi gt tan'(pi)/(4)`
`rArr n/pi gt 1 [:' tan'pi/4=1]`
`rArr n gt pi`
So, the minimum value of `n` is `4`. `[:' n in N` and `pi = 3.14"....".]`
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT EXEMPLAR|Exercise Integrals|62 Videos

  • LINEAR PROGRAMMING

    NCERT EXEMPLAR|Exercise Linear Programming|45 Videos

Similar Questions

Explore conceptually related problems

Find the minimum value of n for which tan^(-1)((n)/(pi))>(pi)/(4),n in N

The value of tan(n pi+(pi)/(3)),n in I is

If cot^(-1)((n)/(pi))>(pi)/(6),n in N, then the maximum value of n is :

Q.if cot ^(-1)((n)/(pi))>(pi)/(6),n in N, then the maximum value of 'n' is

Evaluate tan{(-1)^(n)(pi)/(4)} where n is an integer

The value of the natural numbers n such that 2 ^(n) gt 2n +1 is valid for

The most general value for which tan theta=-1cos theta=(1)/(sqrt(2)) is (n in Z)n pi+(7 pi)/(4) (b) n pi+(-1)^(n)(7 pi)/(4)2n pi+(7 pi)/(4) (d) none of these

If tan x=3cot x, then the general value of x is a.n pi+(pi)/(6),n in I b.n pi+(pi)/(3),n in I c.n pi+-(pi)/(6),n in I d.n pi+-(pi)/(3),n in I

NCERT EXEMPLAR-INVERSE TRIGONOMETRIC FUNCTIONS-Inverse Trigonometric Functions
  1. The number of real solutions of the equation sqrt(1+cos2x) = sqrt(2)...

    Text Solution

    |

  2. If cos^(-1)x gt sin^(-1) x, then

    Text Solution

    |

  3. The principal value of cos^(-1)(-1/2) is

    Text Solution

    |

  4. The value of sin^(-1)(sin'(3pi)/(5)) is "….."

    Text Solution

    |

  5. If cos(tan^(-1)x+cot^(-1)sqrt(3))=0 , find the value of xdot

    Text Solution

    |

  6. The set of values of sec^(-1)(1/2) is "……….."

    Text Solution

    |

  7. The principal value of tan^(-1)sqrt(3) is "……."

    Text Solution

    |

  8. The value of cos^(-1)(cos'(14pi)/(3)) is "…….."

    Text Solution

    |

  9. The value of cos(sin^(-1)x + cos^(-1)x), where |x| le 1, is

    Text Solution

    |

  10. The value of tan((sin^(-1)x+cos^(-1)x)/(2)), when x = (sqrt(3))/(2), i...

    Text Solution

    |

  11. If y = 2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))), then "………"lt y lt "………".

    Text Solution

    |

  12. The result tan^(-1)x-tan^(-1)y = tan^(-1)((x-y)/(1+xy)) is true whe...

    Text Solution

    |

  13. The value of cot^(-1)(-x) x in R in terms of cot^(-1)x is "…….."

    Text Solution

    |

  14. All trigonometric functions have inverse over their respective domai...

    Text Solution

    |

  15. The value of the expression (cos^(-1)x)^(2) is equal to sec^(2)x.

    Text Solution

    |

  16. The domain of trigonometric functions can be restricted to any one o...

    Text Solution

    |

  17. The least numerical value, either positive or negative of angle thet...

    Text Solution

    |

  18. The graph of inverse trigonometric function can be obtained from th...

    Text Solution

    |

  19. The minimum value of n for which tan^(-1)'n/pi gt (pi)/(4), n in N, i...

    Text Solution

    |

  20. The principal value of sin^(-1)[cos(sin^(-1)'1/2)] is pi/3.

    Text Solution

    |