Home
Class 12
MATHS
If tan^(-1)((x-2)/(x-4))+tan^(-1)((x+2)/...

If `tan^(-1)((x-2)/(x-4))+tan^(-1)((x+2)/(x+4))=pi/4`, find the value of `x`.

Text Solution

Verified by Experts

The given equation may be written as
`tan^(-1)(x-2)/(x-4)=pi/4-tan^(-1)(x+2)/(x-4)=tan^(-1)1-tan^(-1)((x+2)/(x+4))[therefore pi/4=tan^(-1)(1/(x+2))`.
`therefore (x-2)/(x-4) =1/(x+3) rArr (x-2)(x+3)=(x-4)`
`rArr x^(2)+x-6=x-4 rArr x^(2)=2 rArr x=+-sqrt(2)`.
Hence, `x=+-sqrt(2)`.
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4A|4 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4B|22 Videos

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions Ii|37 Videos

  • LINEAR DIFFERENTIAL EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|27 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1)((x-3)/(x-4))+tan^(-1)((x+3)/(x+4))=(pi)/(4)

If tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1)/(x+2)=(pi)/(4) ,then find the value of x .

If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=(pi)/(4) then find the value of x

If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=(pi)/(4), then find the value of x.

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

If tan^-1 ((x-1)/(x-2)) + tan^-1 ((x+1)/(x+2)) = π/4 then find the value of x.

Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4

Solve for x : tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4

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

RS AGGARWAL-INVERSE TRIGNOMETRIC FUNCTIONS -Objective Questons
  1. If tan^(-1)((x-2)/(x-4))+tan^(-1)((x+2)/(x+4))=pi/4, find the value of...

    Text Solution

    |

  2. Find the principal value of: cos^(-1)((sqrt(3))/2)

    Text Solution

    |

  3. Find the principal value of the following: (i) cosec^(-1)(2) (ii) ta...

    Text Solution

    |

  4. Find the principal value of: cos^(-1)(-1/(sqrt(2)))

    Text Solution

    |

  5. Find the principal value of: sin^(-1)(-1/2)

    Text Solution

    |

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

    Text Solution

    |

  7. The principal value of tan^-1(-sqrt3) is

    Text Solution

    |

  8. The principal value of cot^(-1)(-1) is

    Text Solution

    |

  9. Find the principal value of sec^(-1)((-2)/(sqrt(3)))

    Text Solution

    |

  10. The principal value of "cosec"^(-1)(-sqrt(2)) is

    Text Solution

    |

  11. Find the principal values of each of the following: cot^(-1)(-sqrt(...

    Text Solution

    |

  12. The principle value of sin ^(-1)(sin ""(2pi)/(3)) is

    Text Solution

    |

  13. The value of cos^(-1)(cos(14pi/6)) is

    Text Solution

    |

  14. The value of tan^(-1)(tan(8*pi/6)) is

    Text Solution

    |

  15. Find the value of : cot^(-1), (5pi/4)

    Text Solution

    |

  16. The value of sec^(-1)(sec(8pi)/5) is

    Text Solution

    |

  17. The value of "cosec"^(-1)("cosec"(4pi)/3) is

    Text Solution

    |

  18. प्रश्न संख्या 16 से 18में दिए प्रत्येक व्यंजन का मान ज्ञात कीजिए : t...

    Text Solution

    |

  19. pi/3-sin^(-1)(-1/2)=?

    Text Solution

    |

  20. The value of sin(sin^(-1)(1/2)+cos^(-1)(1/2))=?

    Text Solution

    |

  21. If x ne 0 then cos(tan^(-1)+cot^(-1)x)=?

    Text Solution

    |