Home
Class 12
MATHS
Find the value of 4 tan^-1 (1/5) - tan^-...

Find the value of `4 tan^-1 (1/5) - tan^-1 (1/239) `

Text Solution

Verified by Experts

The correct Answer is:
N/a
We have, `4tan^(-1)'1/5 - tan^(-1)'1/(239)`
`=2.2tan^(-1)'(1)/(5)-tan^(-1)'1/239`
`=2.[tan^(-1)'((2)/(5))/(1-(1/5)^(2))]-tan^(1)'1/239, [:' 2tan^(-1)x=tan^(-1)((2x)/(1-x^(2)))]`
`= 2.[tan^(-1)((2/5)/(1-1/25))]-tan^(-1)'1/239`
`=2.[tan^(-1)((2//5)/(24//25))]-tan^(-1)'1/239`
`=2tan^(-1)'5/12-tan^(-1)'1/239`
`=tan^(-1)'(2.(5)/(12))/(1-(5/12)^(2))-tan^(-1)'1/239 , [:' 2tan^(-1)x=tan^(-1)((2x)/(1-x^(2)))]`
`=tan^(-1)((5/6)/(1-(25)/(144)))-tan^(-1)'1/239`
`=tan^(-1)((144xx5)/(119xx6))-tan^(-1)'(1)/(239)`
`=tan^(-1)((120)/(119))-tan^(-1)'1/239`
`=tan^(-1)((120/119-1/239)/(1+120/(119).(1)/239)) , [:' tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(x+y))]`
`=tan^(-1)((120xx239-119)/(119xx239+120))`
`=tan^(-1)[(28680-119)/(28441+120)]=tan^(-1)'(28561)/(28561)`
`=tan^(-1)(1)=tan^(-1)(tan'(pi)/(4))=pi/4`
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 value of 4 tan^(-1).(1)/(5) - tan^(-1).(1)/(70) + tan^(-1).(1)/(99)

Find the value of x: tan^-1 x + tan^-1 (1/3) = π/4

Find the value of 4tan^(-1)((1)/(5))-tan^(-1)((1)/(239))

Find the value of 4tan^(-1)(1)/(5)-tan^(-1)(1)/(70)+tan^(-1)(1)/(99)

4 tan^(-1)(1/5)-tan^(-1)(1/239) is equal o

tan^-1 (1/6) + tan^-1 (5/7) = π/4

Find the value of : 4(2 tan^(-1) . 1/3 +tan^(-1). 1/7)

Find the value of sin^(-1) ((3)/(5)) + tan^(-1) ((1)/(7))

The value of tan(2tan^(-1)(1/5))

NCERT EXEMPLAR-INVERSE TRIGONOMETRIC FUNCTIONS-Inverse Trigonometric Functions
  1. Show that sin^(-1)'5/13+cos^(-1)'3/5=tan^(-1)'63/16.

    Text Solution

    |

  2. Prove: tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/sqrt(5))

    Text Solution

    |

  3. Find the value of 4 tan^-1 (1/5) - tan^-1 (1/239)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Which of the following of the principal value branch of cos^(-1)...

    Text Solution

    |

  7. Which of the following is the principal value branch of cosec^(-1)x ?

    Text Solution

    |

  8. If 3tan^(-1)x +cot^(-1)x=pi, then x equals to

    Text Solution

    |

  9. The value of sin^(-1)(cos(33pi)/5) is (3pi)/5 (b) pi/(10) (c) pi/(10) ...

    Text Solution

    |

  10. The domin of the function cos^(-1) (2x-1) is

    Text Solution

    |

  11. The domain of the function defined by f(x) = sin^(-1)sqrt(x-1) is

    Text Solution

    |

  12. If cos(sin^(-1)'2/5 + cos^(-1)x) = 0, then x is equal to

    Text Solution

    |

  13. The value of sin[2tan^(-1)(0.75)] is

    Text Solution

    |

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

    Text Solution

    |

  15. The value of 2sec^(-1) + 2 sin^(-1)(1/2) is

    Text Solution

    |

  16. If tan^(-1) x + tan^(-1) y = (4pi)/(5), then cot^(-1) x + cot^(-1) y ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. The value of tan(1/2 cos^(-1)'2/(sqrt(5))) is

    Text Solution

    |

  20. If |x| le 1, then 2tan^(-1)x + sin^(-1)((2x)/(1+x^(2))) is equal to

    Text Solution

    |