Home
Class 12
MATHS
If tan^(-1) x +tan^(-1) y = pi/4 , xy lt...

If `tan^(-1) x +tan^(-1) y = pi/4 , xy lt 1 ` , then prove that `x+y+xy=1`.

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise Questions From NCERT Exemplar|4 Videos

  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 2 (a) (Short Answer Type Questions)|10 Videos

  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (2)|11 Videos

  • INTEGRALS

    MODERN PUBLICATION|Exercise COMPETITION FILE|24 Videos

  • LINEAR PROGRAMMING

    MODERN PUBLICATION|Exercise Chapter Test|12 Videos

Similar Questions

Explore conceptually related problems

If tan^(-1) x + tan^(-1) y - tan^(-1) z = 0 , then prove that : x+ y + xyz = z .

If tan ^ (- 1) x + tan ^ (- 1) y + tan ^ (- 1) z = pi prove that x + y + z = xyz

If tan^(-1)x+tan^(-1)y+tan^(-1) z=(3pi)/(2) then prove that xy+yz+zx=1

If tan^(-1)x+ tan^(-1)y + tan^(-1)z = pi , prove that x + y + z = xyz .

If tan^(-1)x+tan^(-1)y=(pi)/(4) , and the value of xy<1 ,then show that x+y+xy=1 .

If tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(2) then prove that yz+zx+xy=1

If tan^(-1)x+tan^(-1)y=(pi)/(2), then prove that xy=1

If tan^(-1)x+tan^(-1)y=(pi)/(4), then write the value of x+y+xy.

MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-Frequently Asked Questions
  1. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

    Text Solution

    |

  2. If tan^(-1) x +tan^(-1) y = pi/4 , xy lt 1 , then prove that x+y+xy=1...

    Text Solution

    |

  3. Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

    Text Solution

    |

  4. If sin^(-1) x = tan^(-1)ym what is the value of (1)/(x^(2))-(1)/(y^(2)...

    Text Solution

    |

  5. Prove that cos^(-1)x+cos^(-1) [x/2 +(sqrt(3-3x^(2)))/2 ] = pi/3 ,1...

    Text Solution

    |

  6. Find the value of : sin^() (2 tan^(-1). 1/4) +cos (tan^(-1)2sqrt(2))

    Text Solution

    |

  7. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

    Text Solution

    |

  8. Show that sin^(-1)3/5-sin^(-1)8/(17)=cos^(-1)(84)/(85) .

    Text Solution

    |

  9. Prove that: sin^(-1)((5)/(13))+cos^(-1)((4)/(5))=(1)/(2)sin^(-1)((3696...

    Text Solution

    |

  10. Show that : 2 sin^(-1) (3/5)-tan^(-1) (17/31) = pi/4

    Text Solution

    |

  11. Prove that tan[pi/4+1/2cos^(-1)""a/b]+tan[pi/4-1/2cos^(-1)""a/b]=2b/a

    Text Solution

    |

  12. (9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(4)sin^(-1)""(2sqrt(2))/(3) (...

    Text Solution

    |

  13. Prove that tan^(- 1)((6x-8x^3)/(1-12 x^2))-tan^(- 1)((4x)/(1-4x^2))=ta...

    Text Solution

    |

  14. Prove that tan ^(-1) . 1/5 + tan^(-1) . 1/7 + tan ^(-1) . 1/8 = pi/4

    Text Solution

    |

  15. Solve : 2 tan^(-1), (cos x) = tan^(-1), (2 cosec x)

    Text Solution

    |

  16. Solve : tan^(-1) 4x +tan^(-1)6x = pi/4

    Text Solution

    |

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

    Text Solution

    |

  18. Solve : (i)" "tan^(-1). x/2 +tan^(-1). x/3 = pi/4 , sqrt(6) gt x gt 0...

    Text Solution

    |

  19. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

    Text Solution

    |

  20. Prove that t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

    Text Solution

    |