Home
Class 12
MATHS
If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3ta...

If `(tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y`. Then which of the following may be true

A

`(x+y)/(tan1)=-2`

B

`(tan^(-1)x)/(1-tan^(-1)y)=2`

C

`(x+y)/(tan1)=2`

D

`(x+y)/(cot1)=1`

Text Solution

Verified by Experts

The correct Answer is:
A
`a^(3)+b^(3)+c^(3)=3abc`
`impliesa+b+c=0` or `a=b=c`
`impliestan^(-1)x+tan^(-1)y=1` or `tan^(-1)x=tan^(-1)y=-1`
`impliesx=y=-tan1` or `(x+y)/(1-xy)=tan1`
`(x+y)/(tan1)=-2`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If tan ^(-1)x+tan^(-1)y-sin^(-1)x=0, then which of the following are true?

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

If tan^(-1) 3 +tan^(-1)x=tan^(-1)8 then x =

If tan^(-1)3+ tan^(-1)x = tan^(-1)8 , then: x=

If tan A=(1)/(2) and tan B=(1)/(3) , then which of the following is true ?

If tan^(-1)x-tan^(-1)y=tan^(-1)A, then A=

If: tan^(-1)(1/3) + tan^(-1)( 3/4) - tan^(-1)(x/3) =0 , then: x=

tan^(-1)x+tan^(-1)y=pi+tan^(-1)((x+y)/(1-xy))

If 2tan^(- 1)(c o s e c(tan^(- 1)(x))-tan(cot^(- 1)(x)))=tan^(- 1)y then y is equal to

RESONANCE-TEST PAPERS-MATHEMATICS
  1. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  2. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  3. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  4. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  5. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  6. is The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not ...

    Text Solution

    |

  7. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  8. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  9. Let f(x)=x^(3)-x^(2)+x+1 and g(x)={("max "f(t) 0letlex 0lexle1),(3-x 1...

    Text Solution

    |

  10. The value(s) of x satisfying tan^(-1)(x+3)-tan^(-1)(x-3)=sin^(-1)(3/5)...

    Text Solution

    |

  11. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  12. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  13. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  14. For the curve y=4x^3-2x^5,find all the points at which the tangent pa...

    Text Solution

    |

  15. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  16. If y+a=m(1)(x+3a),y+a=m(2)(x+3a) are two tangents to the parabola y^(2...

    Text Solution

    |

  17. If f(x)=lim(m->oo) lim(n->oo)cos^(2m) n!pix then the range of f(x) is

    Text Solution

    |

  18. Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the srai...

    Text Solution

    |

  19. Q. For every integer n, let an and bn be real numbers. Let function f:...

    Text Solution

    |

  20. Let a and b are real numbers such that the function f(x)={(-3ax^(2)-2,...

    Text Solution

    |